What is 2nd order: Definition and 494 Discussions

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  1. D

    Solve 2nd Order Diff Eq: y''=sin(3t)+4e^t, y(0)=1, y'(1)=0

    Homework Statement find a general solution to the eq: y''=sin(3t)+4e^t Find a particular solution that satisfies y(0) = 1 y'(1) = 0 Homework Equations The Attempt at a Solution ive figured the general solution to be y(x)= -sin(3t)/9 + 4e^t + c + d And thus y'(x) = -cos(3t)/3...
  2. A

    Laplace Transformation of 2nd order step function

    Homework Statement Find the Laplace transform of f(t) where f(t)={ 3 if 0<=t<2 2t^2+2 if 2<=t<3 -4 if t>=3 Homework Equations The Attempt at a Solution We where taught to approach this from a "turn-off, turn-on" strategy where...
  3. D

    General solution to 2nd order DE

    Hi, I am just looking for clarification whether or not I am doing these problems correctly, here's an example: Homework Statement Find the general solution to x'' -2x' + 5x = 0 Homework Equations Charasteristic polynomial. Quadratic equation. General solution form for complex...
  4. D

    Quadratic Interpolation & 2nd Order Diff. Equations

    For a second order differential equation, is it necessary to derive a weak form if quadratic interpolation are used?
  5. M

    Simple 2nd order nonlinear ODE

    I'm trying to solve the equation y'' = x^2 * y. This looks like it should be simple, but I don't have mathematica and the only reference I've found calls it a special case of the Emden-Fowler equation and refers to a solution in a book I don't own. Does anyone know the solution to this...
  6. J

    2nd order linear differential equation (homogeneous)

    Homework Statement Solve 354y`` −692y` + 235y =0 y(0) = 7 y`(0) = 4 Homework Equations The Attempt at a Solution First I divided the equation by 354 to get y`` - 1.56y` + 0.894y = 0. Then I found the roots of this to be 0.94, repeated twice. For repeated roots the solution looks like y=...
  7. W

    Help solving 2nd order differential equation

    Help solving 2nd order differential equation please While solving for the time it takes an object of mass, m, with initial velocity, v, to compress a spring with spring constant, k to the maximum compression, I came across the following differential equation m(d^{2}x/dt^{2}) = kx - mg I...
  8. H

    Can the Parabolic Cylinder Function Solve a 2nd Order D.E. with a Constant?

    Homework Statement \frac{d^2\phi(\eta)}{d\eta^2} = (\eta^2 - K) \phi(\eta) Where K is essentially a constant, K = 2n + 1 (n is an integer). The Attempt at a Solution I don't even know where to begin since \phi is a function of \eta. A push in the right direction would be much...
  9. J

    Stuck on a 2nd order linear differential equation

    Homework Statement y'' - 2y'+ 6y = 0 y(0) = 3 y(5) = 7 Find a solution y(t).Homework Equations The Attempt at a Solution I found the characteristic equation: x2 - 9x = 0, which has roots at 0 and 9. Therefore y(t) = C1e0x + C2e9x Using the initial conditions to solve this: 3 = C1 + C2 7 =...
  10. K

    2nd order linear hyperbolic PDE?

    uxx - x2 uyy = 0 (assume x>0) Is there any systematic method (e.g. change of variables) to solve this hyperbolic equation? dy/dx = [B + sqrt(B2 - AC)]/A => dy/dx = x => 2y -x2 = c dy/dx = [B - sqrt(B2 - AC)]/A => dy/dx = -x => 2y + x2 = k So the characteristic curves are 2y -x2 =...
  11. R

    The Impossible Task of Solving a 2nd Order DE for r(t)

    Suppose an object is moving toward the Earth(with a direction perpendicular to the Earth's surface) at an initial speed v0, starting from a distance r0. The object also experiences gravitational acceleration. Is it possible to obtain an expression of r as a function of t? In other words, what's...
  12. F

    Design an active filter 2nd order

    • No ripple can exist in the output, but non-linear phase shift is allowed. • The frequency response must be as close as possible to the ideal filter response. • Signals of frequency 0 ~ 5 KHz are only allowed to pass through the filter with a desired gain of 4dB . Other frequencies should...
  13. J

    Finite difference for 2nd order PDE

    I need to solve the following PDE: \frac{1}{2}F_{\eta \eta }\sigma _{\eta }^{2}\eta ^{2}+\frac{1}{2}F_{pp}\sigma _{p}^{2}+F_{p}k(m-p)+F_{\eta }a\eta -rF=0 \label{6} where p goes from minus to plus infinity and eta goes from zero to plus infinity. Here p and eta are state variables and all...
  14. P

    Solving 2nd order differential equation with non-constant coefficients

    Hi~ I'm having trouble with solving a certain differential equation. x2y'' + x y'+(k2x2-1)y = 0 I'm tasked to find a solution that satisfies the boundary conditions: y(0)=0 and y(1)=0 I have tried solving this using the characteristic equation, but i arrived at a solution that is...
  15. D

    Series solution to 2nd order differential equation

    when using the power series to solve an ODE, is it always necessary to shift the index to 2 and 1 when taking the second and first derivatives of the power series respectively? i noticed that if i don't shift the index at all and leave them at n=0, it still works out fine? also, how...
  16. M

    Integrating 2nd order derivative

    The question is If f(x) = 7x^3 + 8x^2 - x + 11, evaluate : a, Integral +1 - -1 f(x) dx b, Integral +1 - -1 f'(x) dx c, Integral +1 - -1 f''(x) dx For a, Just integrate each individual and then input the figures which gave me 1.75x^4 + (8x^3)/3 - 0.5x^2 + 11x Which when I input...
  17. T

    2nd Order ODE,Homogeneous,Non-Constant Coeff.

    Hi, I am trying to guess the solution for this i am sure the solution involves a ln(x) so that i can reduce the order to find the general solution but i just can't seem to find it... any suggestions ?? \[ (c_{o}+xk)y''+ky'=0\] with ths usual boundary conditions...
  18. B

    Solving a linear homogenous 2nd order DE with a constant term

    I know how to go about solving differential equations of the form y''+q(x)y'+t(x)y = 0 through the methods of finding the characteristic polynomial of the differential equation and solving for the roots, etc. But what I am not clear on is how I would go about solving an equation like this where...
  19. R

    2nd Order nonhomogeneous ODE using Undetermined Coefficients

    Homework Statement Find General Solution: y"+6y'+9y=e-3x-27x2 Homework Equations The Attempt at a Solution I know you have yh which is the general solution to the left side of the equation set to 0 and then fine the particular solution. When i try to find yp1 I get...
  20. N

    Equivalence of Two Forms of Solutions to Second Order ODEs

    Homework Statement I was curious if anyone could help me prove the equivalence between the two forms of solutions to second order ODEs, one being the linear combination of two solutions and the other being the phase-shifted sin/cos function. Homework Equations...
  21. F

    Nonhomogeneous 2nd order dif question?

    y''-2y''-3y=3e^2t find the general solution I have tried Ate^t, Ate^2, Ate^3 none have worked they all leave extra variables that don't match up. is there another combination I could try?
  22. J

    Fourier transform with mixed derivatives/ 2nd order ODE

    Homework Statement Hi, So I'm suppose to solve the following problem: \left.\frac{d^{2}u}{dt^{2}}-4\frac{d^{3}u}{dt dx^{2}}+3\frac{d^{4}u}{dx^{4}}=0 \left.u(x,0) = f(x) \left.\frac{du}{dt}(x,0) = g(x) Homework Equations The Attempt at a Solution First I use Fourier transform on...
  23. M

    How do I solve a 2nd order nonlinear ODE with specific boundary conditions?

    Hi, I need some help, I must solve the following nonlinear differential equation, -k1*(c'') = -k2*(c^0.5) - u*(c') subject to the bc, u*(c - 0.5) = k1*(c') where k1, k2, and u are constants, thanks
  24. E

    How to solve 2nd order non-linear DE with exponential

    Hi, Does anyone knows how to solve this 2nd order non linear differential equation with exponential components? d"V/dx" = A*exp(-B*V)-C*exp(B*V) where A, B, C are constants. Thanks
  25. T

    Can it be 2nd order non-linear diff. equation

    Hope I have posted this in the right section, this question is half differential equation and half finite difference method. The equation I have is a form of the Lucas Washburn equation, which is concerned with capillary rise...
  26. P

    2nd order nonlinear non-seperable equation

    I've recently been trying to solve the following equation: d2x/dt2 + (x2 - a) dx/dt + (x2 - b)x = 0 I've reduced it to a first order equation by a simple substitution of y = dx/dt to obtain: dy/dx = (a-x2) + [(b-x2)x]/y = 0 However I cannot figure out how to solve this equation. Is it...
  27. H

    2nd order differential equation

    Hi i need some help with solving this equation2 d2y/dt2 + dy/dt +10y = 3sin(9t) - 8e-2t - 7 when y=0 dy/dx = 10 t=0 The bit i am not sure about is the -8e-2t - 7 bit on the right side because i only know how to deal with 2nd order differential equations when they are of the form a d2y/dt2...
  28. F

    Solving 2nd Order Laplace DE: f(t)

    Homework Statement f"(t)-f'(t)-2f(t)=12H0(t-3), f(0)=f'(0)=0 relevant equations, are the laplace transform equations.. H0(t-a)=e-as/s The Attempt at a Solution LT:s2F(s)-sF(s)-2F(s)=12e-3s/s =>F(s)=12e-3s/s(s+1)(s-2) ok now from here, I am lost, i can't do partial fractions can I? and i need...
  29. N

    Laplace Transform of 2nd Order ODE

    Homework Statement This is a problem from my book that I'm very close to finding the solution to, but I'm a little off. I have a feeling it's some small error I'm just overlooking because I'm so hungry/sleep-deprived. Anyway, the question asks you to find the Laplace transform of the given...
  30. L

    Calculating 2nd Order System Parameters in MATLAB

    What are the commands to i find the peak time, seetling time, rise time and maximum overshoot of a second order system in matlab?
  31. S

    How to solve 2nd order ODE solution eg. te^t+e^t, for t?

    Hi, I have a second order differential equation with a solution in the form: f(t) = Ae^{t}+Bte^{t} I want to solve for t, ie. work out for what value of t does the function f(t) have a particular value. But there seems to be no way (that I know of) to do this. Can anyone give me any...
  32. S

    ODE ( 2nd order nonhomogeneous equation)

    Homework Statement By using the method of undetermined coefficients,find the particular solution of y''+y'+y=(sin x)^2 Homework Equations i know how to determine the particular solution IF it is sin x. Ex: sin x ====> Asin x + B cos x (particular) but i wonder how to determine the...
  33. N

    Is GR a 2nd order approximation in g?

    While studying the Einstein Equation, I noticed something curious, at least to me with little experience in General Relativity. Start with the usual formulation of the equation: R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8{\pi}G}{c^2}T_{\mu\nu} Then, apply the...
  34. Z

    2nd order dampened harmonic oscillator (Shot in the dark)

    I have the following equation subject to y(0)=0 and y'(0) = 0 my'' + b y' + k y = C I have done an experiment where I measured force at given depth for a dampened harmonic oscillator. Is it possible to use the force I measured to solve for displacement and then back out coefficient b for...
  35. D

    2nd order ode w/complex conjugate roots

    x''+x'+2x=0 x(0)=2 x'(0)=0 I've taken the characteristic equation and reduced the roots to 1/2 +- Sqrt(7/4)i of the form a +- bi (i = sqrt(-1) Then i put the homogeneous solution into the form of e^{}at*(B1cos(bt)+B2sin(bt)) for B1 i used the first i.c. and found that B1=2...
  36. D

    Solving 2nd Order Differential Equation with Dirichlet BCs

    Homework Statement Solve: -D(x) \frac{d^2 T}{dx^2}=1 for x \in [0,1] D(x) =10-3 in [0,0.5] and D(x) = 1 in (0.5,1] with homogeneous dirichlet boundary conditions The Attempt at a Solution So I have two quadratic equations with x(0)=x(1)=0 and continuity at x=0.5 but I'm...
  37. T

    Help with Laplace Transformations and 2nd order ODEs

    Homework Statement Solve the following problems using Laplace Transforms: y' - y = 2e^t, y_0 = 3 y'' + 4y' + 4y = e^{-2t}, y_0 = 0, y_0' = 4 y'' + y = sin(t), y_0 = 1, y_0' = 0 y'' + y = sin(t), y_0 = 1, y_0' = -\frac{1}{2} Homework Equations N/A The Attempt at...
  38. Somefantastik

    Solving 2nd Order PDE: u_{xx} - u_{tt} - au_{t} - bu = 0

    the book gives u_{xx} - u_{tt} - au_{t} - bu = 0; 0<x<L, t>0 says if you multiply it by 2u_{t} you can get \left( 2u_{t}u_{x}\right)_{x} - \left( u^{2}_{x} + u^{2}_{t} + bu^{2}\right)_{t} -2au^{2}_{t} = 0 or \frac{\partial}{\partial x} \left( 2 \frac{\partial...
  39. M

    2nd Order Derivative Applications

    Homework Statement This is a discussion question from an online course I'm taking. 1. Find an example from engineering which involves a second order derivative. This 2nd order derivative should have some name. For example, the 2nd derivative of displacement with respect to time is called...
  40. S

    Nonhomogeneous 2nd order DE

    Homework Statement y'' + 9y = 2x2e3x + 5 Homework Equations N/A The Attempt at a Solution I think the complementary solution yc = c1cos(3x) + c2sin(3x). If not for that little +5 at the end of the right hand side, I'm pretty sure I could solve it. But I don't know how to include it in my...
  41. D

    Linear transformation of a 2nd order pde

    First off I am NOT asking you to solve this for me. I'm just trying to understand the concept behind this problem. Let L be a linear transformation defined by L[p]=(x^2+2)p"+ (x-1)p' -4p I have not seen linear transformations in this format. Usually I see something like L(x)=x1b1+ x2b2...
  42. E

    2nd order differential equation using reduction of order

    Homework Statement Use the method of reduction of order to find a second solution of the given differential equation t2y'' - 4ty' + 6y, t>0; y1(t) = t2 The Attempt at a Solution Here's what I have so far: y = vt2 y' = 2tv + t2v' y'' = 2v + 4tv' + t2v'' so t2 (2v + 4tv'...
  43. M

    Linear 2nd order diff. eqn.

    1. This is exercise 3.19.15 from Boyce & DiPrima's Differential Equations. u'' + u = F(t), u(0) = 0, u'(0) = 0 0 \leq t < \pi , F(t) = F_0t \pi \leq t \leq 2\pi , F(t) = F_0(2\pi-t) t > 2\pi , F(t) = 0 Solve for u(t) . 2. The solution to the homogenous equation is...
  44. O

    2nd order non-homogenous differentila equation

    I have to start from a simple 2nd order ordinary deifferential equation as: y’’+2ξωny’+ω2y = F The solution should be of the form y = ∫F(Ω) G(t - Ω) dΩ (integral from 0-t) where G(t) = 1/ω * e^(-ξωnt)sin(ξt) for ξ<1 G(t) = e^(-ωnt) for...
  45. B

    2nd order ODE with constant coefficients and tricky RHS

    Homework Statement \frac {d^2x} {dt^2} -x = te^{-t} Find the general solution (I only need help on finding the particular solution). Homework Equations Well, I can easily find the complimentary solution via the characteristic equation, my problem lies in the particular solution...
  46. S

    Lagrangian method for nonlinear ODE, 2nd order ?

    Lagrangian method for nonlinear ODE, 2nd order ?? I have to solve non-linear ODE of 2nd order. The Maple routines can't find integrating factor. I think that's connected to Lie symmetries that can't be found. I'm thinking of getting a Lagrangian for which that equation is the Euler-Lagrange...
  47. R

    Converting 2nd order ODE to Bessel Function

    Homework Statement I am attempting to solve the 2nd order ODE as follows using the generalized solution to the Bessel's equation Homework Equations original ODE: xd^{2}y/dx^{2}-3dy/dx+xy=0 The Attempt at a Solution My first thought is to bring out an x^-1 outside of the function so...
  48. A

    Condition for a 2nd order differential eqn to have bounded solutions?

    Suppose I have a 2nd order differential equation a_1y''(x)+a_2y'(x)+a_3y(x)+a_4=0 and two conditions y(0), y'(0). Then is there any theorem which gives us the condition under which the solution y(x) will be bounded? Note that x-range is entire real line. This is a general version of the...
  49. Y

    Solution of the nonlinear 2nd order differential equation

    Homework Statement I'd like to solve the following non-homogeneous second order differential equation and may I ask smart scholars out there to help me with this? y"(1-1.5(y')^2)=Cx^n, (^ denotes "to the power of") where C and n are constants, and the boundary conditions are: y=0...
  50. P

    From 2 1st order ODEs to 1 2nd order ODE?

    Hi, it is well known that a second order ODe can be transformed into a system of two ODEs through the transformation u=y', v= y. Is the other way round possible? I mean, I have a system of 2 ODEs and want to transform it into a sucession on higher order problems that can be solved one after...
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