What is 2nd order: Definition and 494 Discussions

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  1. M

    Can These Second Order ODEs Model Planetary Trajectories?

    Hello everybody! Here are two ODE 2nd order I tried to solve, but I failed :( r''[t] - k/(r[t])^2 = 0 xy''[x] = ay[x] + b Could anyone of you please help me? Thanks in advance :)
  2. P

    2nd order partial differential equation

    Hello all, this is my first post and I'm having trouble with some homework. Here is the problem: Solve: U_x_y - yU_y = e^x I tried subbing V = U_y then I have V_x - yV = e^x I solve this as a linear equation with an integrating factor of e^{-\frac{1}{2}y^2} and get V =...
  3. T

    MATLAB 2nd Order Non-Linear ODE in MATLAB Issues

    Hey everyone, Having some trouble here using the solver we were supplied and modifying it to fit our problem... I have a wire with a current flowing through it. I'm trying to find the temperature distribution wrt. position in the wire. BV's are: T(x=L/2) = 300K dT/dx (x=0) = 0 (Apparently...
  4. Y

    Solution to the nonlinear 2nd order d.e

    Hello: Can anyone help me solve with the following nonlinear 2nd order differential equation? d^2 y/dx^2 (1+a(dy/dx)^2)=bx^c (a,b & c are constants.) Thank you. younginmoon
  5. L

    Solving 2nd Order DE: y''+4y'+5y=0 & y(0)=1, y'(0)=0

    Homework Statement I had to solve the 2nd order d.e y'' + 4y' + 5y=0 Which I have done, then I need to find a solution for which y(0)=1 and y'(0)=0 The Attempt at a Solution My general soltuion for the d.e is y= e^(-2x) (c_1 *cos(x) + c_2*sin(x)) so for y(0)=1= e^0 (c_1 * 1 +...
  6. L

    How to solve 2nd order d.e ? Is this the right start?

    Homework Statement find the general solution of y' = (y + y^2)/(x + x^2) The Attempt at a Solution I've tried a number of ways the first most obvious way I figured was to multiply the x+x^2 over so I did that but then when I expand I end up with a y' in both of the terms and I...
  7. R

    2nd order differential equations with constant coeff. The Particular integrals.

    For the differential equation \frac{d^2y}{dx^2}+4 \frac{dy}{dx}=sinx One root of the auxiliary equation is '0' meaning the particular integral for the right hand side is x(Asinx+Bcosx). But is there any formal proof for making this claim that for 0 as one root is it is x(Asinx+Bcosx) or...
  8. F

    Solving for 2nd Order LODE System: Component Form and Eigenvectors

    Homework Statement Solve the following system for \mathbf{r}(t): \frac{d^2\mathbf{r}}{dt^2}=-\frac{k}{m}\mathbf{r}.Homework Equations The Attempt at a Solution Now, I know how to solve for the magnitude of r (in fact, since it's the equation for the simple harmonic motion of a spring obeying...
  9. A

    2nd order with exponential and constant on right side

    Hi everybody, How do I solve this differential equation ??: y'' = a(Exp(-b*y)-1) ; where a, b are constants with the boundaries conditions : y'(x=0)=-K1 y'(x=L)=0 without the constant term I can do y''*y' = y' a Exp(-b y) then integrate it \ {1/2} (y')^2= {a/b}...
  10. F

    General solution to 2nd order ODE

    Find the general solution of the ordinary differential equation. y'' - 7y'+ 6y = 2e^(3t) + te^(t) First i found GS(H) by lettings y = e^(cx) and got GS(H) = Ae^(6t) + Be^(t) i then found PS(IH) y'' - 7y'+ 6y = 2e^(3t) by letting y = ae^(3t) and got PS(IH) = -(1/3)e^(3t) Now my...
  11. T

    How to solve this 2nd order nonlinear differential equation

    Hello all, This is the first time I've stumbled across this site, but it appears to be extremely helpful. I am a meteorology grad student, and in my research, I have run across the following 2nd order non linear differential equation. It is of the form: y'' + a*y*y' + b*y=0 where a...
  12. M

    Is it 2nd order polynomials, or 2nd order quadratics?

    I thought this was rather odd, and wanted to just show it to see what you all thought of it. Well, also, if anyone knows what I should read to exactly understand what I did. 1: Let's define each answer of a polynomial such as (ax + b)(cx + d) as x1 = (-b/a), x2 = (-d/c). 2: The...
  13. T

    2nd order logic and mathematics?

    Does most of mathematics use 2nd order logic? If so would studying the foundations of mathematics involve mostly using 2nd order logic?
  14. W

    What are the steps for solving a 2nd order differential equation?

    Homework Statement http://img178.imageshack.us/img178/6444/scan0001abq4.th.jpg Homework Equations The Attempt at a Solution this isn't a straight forward calculate the soltion to a 2nd ode so I am pretty stumped.
  15. A

    2nd Order Diff Eqn. (complex roots)

    Homework Statement Prove that if y1 and y2 have maxima or minima at the same point in I, then they cannot be a fundamental set of solutions on that interval. Homework Equations Do I take the wronskian (determinant of y1, y1', y2, y2')? What would that tell me? The Attempt at a Solution
  16. A

    2nd Order Linear Diff. Eqn (homogeneous)

    Homework Statement Show that id y = x(t) is a solution of the diff. eqn. y'' + p(t)y' + q(t)y = g(t), where g(t) is not always zero, then y = c*x(t), where c is any constant other than 1, is not a solution. Homework Equations Can someone help me get started? Also, since g(t) is not...
  17. B

    Conversion of System of Eq's to 2nd Order Diff Eq

    My question is in regards to converting a system of differential equations into a higher order differential equation. I am an undergrad taking diff eq and have just learned the wonders of Euler's method of solving 2nd order differential equations with constant coefficients. It is significantly...
  18. R

    Problem solving 2nd order ODE not for the faint of heart

    Problem solving 2nd order ODE...not for the faint of heart! Hey folks, I'm having problems solving the following set of ODE's: 3H_a^2+H_b^2+6H_aH_b=k_1\rho eq.1 \dot{H_a}+3H_a^2+2H_aH_b=k_2\rho eq.2 \dot{H_b}+2H_b^2+3H_aH_b=k_3\rho eq.3 These are cosmological equations. Note...
  19. qspeechc

    Numerical Solution to 2nd Order Eqn?

    Is there a numerical method for finding solutions to 2nd order non-homogeneous differential equations? Thanks.
  20. C

    2nd order diff Eq help

    2nd order diff Eq with t missing I am trying to find y as a function of t and y'' - y = 0 The two IV given are y(0) = 7, and y(1) = 5 .. Remark: the initial condition involves values at two points. Well since y = {y,y''} and the independent variable t does not appear, I went about it by...
  21. K

    2nd order differential equations

    1) Assume that p and q are continuous on some open interval I, and that y1 and y2 are solutions of y'' + p(t)y' + q(t)y = 0 on I. a) Prove that if {y1, y2} form a fundamental set of solutions on I, then they can't have a common inflection point in I, unless p and q are both 0 at this point...
  22. J

    How to Modify Y(t) for Nonhomogenous 2nd Order DE with e^-t and cos(2t) Terms?

    Homework Statement Well I've got another one that totally sucks. y'' + 2y' + 5y = 4e^{-t}cos(2t) Homework Equations The Attempt at a Solution I tried Y(t) = Ae^{-t}cos(2t) + Be^{-t}sin(2t) but that unfortunately yielded 0 = 4e^{-t} cos(2t) So my question is how does one modify Y(t) in this...
  23. S

    MATLAB How to Solve 2nd Order ODEs in MATLAB?

    Ok, so while I understand 2nd Order ODEs... I really don't understand MATLAB. I have 2 questions that I just can't get any code to work for: 1 Question: Consider the model of an undampened spring-mass system with a time-dependent spring constant k(t) given by: d2y/dt2 + k(t)y = 0...
  24. W

    2nd order differential - particular solution

    [SOLVED] 2nd order differential - particular solution Homework Statement a) Find the general solution of the differential equation: \[2\frac{{d^2 x}}{{dt^2 }} + 5\frac{{dx}}{{dt}} + 2x = 2t + 9\] b) Find the particular solution of this differential equation for which: \[x =...
  25. J

    Solving this 2nd order DE without numerical methods

    Hello, Any ideas on how one would go about attempting to solve this set of equations (for x and y and lambda) without numerical methods. Is it possible, even just to get a approximate solution? Is a set of two 2nd order DE's, \ddot{x} - \dot{x} + xy/R - y^{2} tan(lambda) -...
  26. S

    How can I approximate a 2nd order ODE using 4th order Runge-Kutta?

    Homework Statement Hey, I am trying to approximate the solution to a second order ODE using the 4th order Runge-Kutta. I was told that in order to do this, I have to write the second order ODE and a pair of 1st order ODEs. Given that my differential equation is d^2v/dt^2 + adv/dt...
  27. I

    2nd order linear non-homogeneous ODE - having trouble

    1. Homework Statement : This problem is in regard to a suspension system (mass, spring, dashpot) subjected to a 2 cm bump in the road. Given the mass and spring coefficient, we are to find: a) The minimum damping coefficient, c, to avoid oscillation. b) The expression for amplitude of...
  28. R

    Particular integral question with 2nd order diff eq'ns

    If there is a differential equation to solve of the form a\frac{d^2y}{dx^2} +b\frac{dy}{dx} + cy = tan(x) you would put the LHS=0 and get the complementary function. But what would the the particular integral of tan(x) ?
  29. A

    Designing a Second Order Passive LPF: Tips and Insights

    This isn't really an exact homework problem since it's for a report I'm doing. Basically, I was wondering what the design for a second order passive low pass filter looks like. I know how to design a regular first order circuit but I have no clue about a second-order PASSIVE LPF. I tried...
  30. K

    What's the mistake in finding a particular solution for a differential equation?

    Homework Statement y''-2ay'+a^2y=e^ax Find a general solution 2. The attempt at a solution I've found the general solution of the homogeneous eq: Ce^ax+Dxe^ax Next, I must find a particular solution on the form Be^ax (*), right? The derivative of (*) is Bae^ax and the 2nd...
  31. T

    2nd Order DE with undamped motion

    Homework Statement Solve the initial value problem u\prime\prime+u=0.5cos (0.8t)\\ u(0)=0 \ u\prime(0) = 0 Homework Equations u(t) = [A*cos (w_nt)+ B*sin (w_nt)] + \frac{F_0}{m(w^2_n-w^2)} \left\{\begin{array}{cl} sin(wt)\\ cos(wt) \end{array}\right. The Attempt...
  32. R

    Real quick question on 2nd order differential equation

    Homework Statement How do I go about solving d^2\theta/dt^2+ (g/L) \theta= g? It's been 2.5 years since I had diff eq. Homework Equations ^ The Attempt at a Solution I don't know. I've spent the past 2 hours going through old books and searching online and still can't figure it out :frown:
  33. H

    2nd order ordinary differential equation for damped harmonic motion

    Homework Statement the equation of motion for a damped harmonic oscillator is d^2x/dt^2 + 2(gamma)dx/dt +[(omega0)^2]x =0 ... show that x(t) = Ae^(mt) + Be^(pt) where m= -(gamma) + [(gamma)^2 - (omega0)^2 ]^1/2 p =-(gamma) - [(gamma)^2 - (omega0)^2 ]^1/2 If x=x0 and...
  34. T

    Proving 2nd Order Differential Eqns

    Homework Statement If y = (3x)/e^2x, find the value of x when d^2y/dx^2 = 0 Homework Equations I'll just abbv d^2y/dx^2 as d2ydx2 The Attempt at a Solution I kept getting stuck at: d2ydx2 = 6/e^2 When d2ydx2 = 0, 6/e^2 = 0 6 = e^2 Then where's my x?? :confused: :confused...
  35. M

    Linear, nonhomogenous, 2nd order ODE IVP

    Homework Statement y''+4y=t^2+3e^t y(0)=0 y'(0)=2 Homework Equations CE: r^2+4 r=+/-2i gs: y=c1 cos(2t) + c2 sin(2t) The Attempt at a Solution guess: yp=(At^2+Bt+C)e^t yp'=At^2e^t+2Ate^t+Bte^t+Be^t+Ce^t yp''=At^2e^t+4Ate^t+Bte^t+2Ae^t+2Be^t+Ce^t back into problem...
  36. B

    Differential equations - 2nd order euler eq'n

    (a) Let alpha (a) and beta (b) be given constant. show that t^r is a solution of the Euler equation t^2 d^2y/dt^2 + at dy/dt + by = 0 , t>0 if r^2 + (a-1)r + b = 0 (b) suppose that (a-t)^2 = 4b. Show that (ln t)t^(1-a)/2 is a second solution of Euler's equation. please help, i have no idea...
  37. B

    Differential equations - 2nd order homogenous eq'n w/ unknown

    Given that the equation t d^2y/dt^2 - (1+3t) dy/dt + 3y = 0. has a solution of the form e^ct, for some constant c, find the general solution (The answer is y(t) = c1(1+3t) + c2e^(3t) Edit: I finished this question as i figured it out. but when i come down to the last step, i get this y1(t) =...
  38. B

    Differential equations - 2nd order nonhomogenous eq'n

    differential equations - 2nd order homogenous eq'n sorry the title should read 2nd order homogenous eq'n, not nonhomogenous Find the general solution of the equation: (1+t^2)d^2y/dt^2 - 2t dy/dt + 2y = 0, given that y1(t) = t is one solution. My attempt: divided equation by 1+t^2...
  39. F

    2nd order DEQ: conserved quantity pt 2

    Homework Statement Consider y'' = - sin(y) find a conserved quantity for this equation Homework Equations This looks an awful lot like a simplified version of a nonlinear pendulum equation The Attempt at a Solution For a conserved quantity I guessed: E = -cos(y) + y' because...
  40. F

    2nd order DEQ: weird solution method

    Homework Statement Suppose that u(t) is a solution to y'' + p(t)y' + q(t)y = 0 Suppose a second solution has the form y(t) = m(t)u(t) where m(t) is an unknown function of t. Derive a first order linear differential equation for m'(t). Suppose y(t) = e^(2t). Use the method...
  41. F

    2nd order DEQ, conserved quantity

    Homework Statement Given: y'' - y - (y^3) = 0 (equation 1) E = (1/2)(v^2) - (1/2)(y^2) - (1/4)(y^4) (equation 2) v = y' i. Show that E is a conserved quanitity ii. Find all the solutions with E = 0 2. The attempt at a solution I'm not sure how to show a...
  42. B

    Differential equation - 2nd order diff equation

    Consider the equation 2t^2y'' + 3ty' - y = 0 (a) Show that y1(t) = sqrt(t) and y2(t) = 1/t are soltuions of the equation on the interval 0<t<infinity (b) Compute W[y1,y2](t). What happens as t approaches zero? (c) Show that y1(t) and y2(t) form a fundamental set of solutions of the equation...
  43. S

    Solving 2nd Order Differential Equation: y'' - 4y = 0

    Homework Statement y'' - 4y = 0 when y = 1, y' = -1, x = 0 2. The attempt at a solution y'' - 4y = 0 m^2 - 4 = 0 m = 2, m = -2 Substituting: y = 1, x = 0 1 = C1 + C2 C1 = -C2 + 1 Substituting: y' = -1, x = 0 -1 -C2 + 1 + C2 C2 = C2 Therefore: y = -C2e^2^x +...
  44. G

    How Do You Solve a Homogeneous Differential Equation with Repeated Roots?

    Never mind, I figured it out. Here's the question: Find the general solution to the homogeneous differential equation https://webwork.math.uga.edu/webwork2_files/tmp/equations/59/540a7a16e5c4e841a098d9d2a72f0a1.png The solution has the form...
  45. K

    2nd order differential equation

    I am currently solving a physics problem that requires me to solve the following equation m(d^2x/dt)=-gamma-c(dx/dt) but I can't seem to come up with a method that makes sense. Note: Gamma is just some constant. I tried to integrate both sides wrt t but then I end up with both a velocity...
  46. U

    Solving a 2nd order ODE using Green's Function

    Homework Statement The homogeneous Helmholtz equation \bigtriangledown^2\psi+\lambda^2\psi=0 has eigenvalues \lambda^2_i and eigenfunctions \psi_i. Show that the corresponding Green's function that satisfies \bigtriangledown^2 G(\vec{r}_1, \vec{r}_2)+\lambda^2 G(\vec{r}_1...
  47. B

    Solving 2nd order inhomogeneous equation

    Let's say that I solve a inhomogeneous differential equation of the type d2y/dx2+k*dy/dx = g (k and g being constants) ..and I get the complementary function: y = A + Be^-kx What would the suggested form of the particular solution be? "Cx" ?
  48. R

    2nd order differential equations I'm so screwed

    Homework Statement Uxx +u(x,y)=0 Homework Equations ? The Attempt at a Solution Step 1) u(x,y)=A(x)B(y) Step 2) uxx=d^u/dx^2 Step 3) d^u/dx^2 + A(x)B(y) = 0 Step 4) d^u/dx^2 = -[A(x)B(y)] (?) I have no idea what I'm doing, so small words would be useful.
  49. A

    Solving a Separable 2nd Order Differential Equation

    In an investigation of a physics problem, I ran into the following equation: d^2(y)/(dt)^2 = k * y * (y^2 + c)^-1.5 I know how to solve separable first order differential equations but this one seems to be beyond me. Assistance?
  50. A

    Understanding Time-Dependent Perturbation Theory's 2nd Order Term

    Time dependent perturbation theory... second order term... For some reason they replace <E_{n}|H_{0}^2|E_{m}> with \Sigma<E_{n}|H_{0}|E_{i}><E_{i}|H_{0}|E_{m}> I know why they are allowed to do this, what I don't understand is how it makes my life better?
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