What is 2nd order: Definition and 494 Discussions

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  1. D

    2nd Order ODE Initial Value Proof Problem

    [b]1. Check that y(t)=1/λ ∫_0-t_〖f(s) *sin(λ(t-s) )ds〗 is the solution of the following initial value problem y''(t)+λ^2y(t)=f(t), λ>0, y(0)=0,y'(0)=0 Homework Equations [b]3. I tried to do integration by parts on y(t), but...
  2. A

    System of three, 2nd order diff. equations

    While trying to solve a problem in physics I got this system of 3, second order differential equations. Solution should be equation for linear harmonic oscillator. m\ddot{η}1+kη1-kη2=0 mn\ddot{η}2-kη1+2kη2-kη3=0 m\ddot{η}3-kη2+kη3=0 My attempts at the solution produced 6th order...
  3. K

    Help needed for solving 2nd order differential equation

    can someone help me solve the differential equation that takes the following form? y''+Ay'+By+Cy^2=f(x), y is function of x Thanks a lot!
  4. I

    Solving a nonhomogeneous 2nd order ode

    Hi, everyone! This is my first post here, I need an hand with this equation! Homework Statement Solve the initial value problem: \begin{equation} \begin{cases} u''(x)+4u(x)=\cos(2x) \\u(0)=u'(0)=1 \end{cases} \end{equation} The Attempt at a Solution I started by solving the...
  5. R

    2nd Order In-Homogeneous Particular Solution?

    Did it :)
  6. S

    Solving 2nd Order ODE: y'' + 2y' - y = e^{-x}, y(0) = y'(0) = 1

    Homework Statement Consider the following second order ODE $$ y'' + 2y' - y = e^{-x}, \quad y(0) = y'(0) = 1. $$ Convert this to a system of first order equations and use the pc33assisys MATLAB file to compute the solution for y(2). Homework Equations The Attempt at a Solution...
  7. P

    2nd order nonhomogeneos differential equations with initial conditions

    Homework Statement The problem states d^2y/dt^2 +15y= cost4t + 2sin t initial conditions y(0)=y'(0)=0 Homework Equations The Attempt at a Solution All I have is this r^2+15=0 making r(+-)=√15 and making yh= C1cos√15+C2√15 the next part includes solve for...
  8. P

    2nd order nonhomogeneos differential equations with initial conditions

    I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem. d^2y/dt^2 +15y =cos 4t+2 sin t this is what I got so far r^2+15=0 for the homogeneous part r=+-(√15) Yh=C1cos√15+C2sin√15 now is...
  9. dexterdev

    MATLAB How to simulate 2nd order markov chain (if poss. Nth order) in MATLAB

    Hi PF, I would like to simulate N th order markov chain (not by means of hidden markov models, but ordinary markov chain) using Matlab. If n-th order is a heavy thing atleast 2nd or 3rd order will do. TIA
  10. D

    2nd order pertubation theory of harmonic oscillator

    Homework Statement I'm having some trouble calculating the 2nd order energy shift in a problem. I am given the pertubation: \hat{H}'=\alpha \hat{p}, where $\alpha$ is a constant, and \hat{p} is given by: p=i\sqrt{\frac{\hbar m\omega }{2}}\left( {{a}_{+}}-{{a}_{-}} \right), where {a}_{+} and...
  11. J

    Coupled 2nd Order DE: Convert to system of 1st Order

    It's been a while since I've played with systems of ODEs, and I seem to have forgotten some of the tricks. As an example, I have two coupled nonlinear DE that I want to convert to a system of four 1st order nonlinear DE. But, the normal way of making variable substitutions is not working of...
  12. H

    Upwinding method for convection terms 2nd order PDE

    I'm trying to solve the equation $$ \frac{\partial u}{\partial t} + \frac{\partial}{\partial x}\left(Cu\right) - \frac{\partial}{\partial x}\left(D\frac{\partial u}{\partial x}\right) = f(x,t) $$ where C and D allow for linearity. I'm using a discontinuous Galerkin method in space and...
  13. D

    2nd order DE for planet's density

    Homework Statement I attached the problem because it's easier Homework Equations The Attempt at a Solution The main problem I have with this problem is trying to find the density as a function of radius. I have been thinking for hours but can't come up with anything. What I...
  14. M

    2nd order differential eguation

    Homework Statement Here is the problem, verbatim. Observe that y=x is a particular solution of the equation 2x^2y''+xy'-y=0[\tex] and find the general solution. For what values of x is the solution valid? Homework Equations The Attempt at a Solution I know the answer is...
  15. C

    How to solve 2nd order diff. equation for simple harmonic motion

    In my physics class we're talking about LC and LRC circuits, and the equations are analogous to those for SHM. However, I don't see how x=Acos(ωt+\varphi) satisfies m(d^2x/dt^2)+(k/m)x=0. I've never done differential equations and in the book it seemed like the author just guessed and checked...
  16. K

    2nd order DE question :confused:

    Homework Statement The equation for the undamped motion with no rubber band: y" + k1y = -10 k1 = any number between 12 and 13 Find exact solutions using a couple different initial conditions And then plot this phase plane using some software The Attempt at a Solution So I know...
  17. D

    Integrating factor for a 2nd order homogeneous linear ODE

    Homework Statement Consider the general linear homogeneous second order equation: P(x)y'' + Q(x)y' + R(x)y = 0 (1) We seek an integrating factor μ(x) such that, upon multiplying Eq. (1) by μ(x), we can write the resulting equation in the form [μ(x)P(x)y']' + μ(x)R(x)y = 0...
  18. R

    Solving a 2nd Order Differential Equation with Initial Conditions

    Homework Statement \frac{d^2 y}{dx^2}\cdot\frac{dy}{dx}=x(x+1), \hspace{10pt} y(0)=1, \hspace{5pt} y'(0)=2 Homework Equations None I can think of... The Attempt at a Solution The only thing I even thought to try was turn it into the form: \frac{d^2 y}{dx^2}{dy}=x(x+1){dx}...
  19. D

    Mathematica Data from 2nd order ode mathematica

    How can I extract time data from a system 2nd order ODEs in Mathematica?
  20. S

    Numerical Integration of 2nd Order DE

    I am intending to use Runge Kutta 4th order to numerically solve a system of coupled equations: \frac{d^{2}x}{dt^{2}} = K1 * x * cos(t) + ( (K2 * \frac{dy}{dt}) - \frac{dz}{dt} ) \frac{d^{2}y}{dt^{2}}= -K1 * y * cos(t) + ( (K2 * \frac{dz}{dt}) - \frac{dx}{dt} )...
  21. D

    MHB How to Convert a 2nd Order ODE System to 1st Order with Consistent Units?

    \begin{alignat*}{3} m\ddot{x} & = & -c(y)\sqrt{x^2+y^2}x\\ m\ddot{y} & = & -mg - c(y)\sqrt{x^2 + y^2}y \end{alignat*} where $c(y) = 0.25\text{N}\cdot\text{s}^2/\text{m}^4\cdot (15\text{cm})^2\exp(-y/(10000\text{m}))$ In order to re-write this as a system of 1st order ODEs, do I have to put...
  22. S

    What is the general solution to the 2nd order linear ODE xy''+2y'+4xy=0?

    Homework Statement Find general solution to: xy''+2y'+4xy=0 Homework Equations Frobenius Method or Bessel's Equation The Attempt at a Solution I know how to get the roots for this problem (which are r1 = 0 & r2 = -1). But not I don't know what to do with these roots. I know that...
  23. D

    MHB Following on to ODE thread 2nd order to 1st

    I am getting this error in Mathematica from the code below: Computed derivatives do not have dimensionality consistent with the initial conditions ClearAll["Global`*"] \[Mu] = 398600; s = NDSolve[{x1'[t] == x2[t], y1'[t] == y2[t], z1'[t] == z2[t], x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 +...
  24. D

    MHB Converting Second Order to First Order: A Systematic Approach

    Can this second order be changed into a system of first order: $$ x''(t) = -\frac{\mu}{(\sqrt{x^2+y^2+z^2})^3}x $$
  25. H

    2nd order mass, spring damper in series

    1. Homework Statement B, K, M 2. Homework Equations 1. xs(t) -----spring ----mass-----damper-----fixed, derive DE for x of mass given :2. F - > M -----spring-------damper ---- fixed in series, derive the DE for velocity of spring 3. The Attempt at a Solution 1. ma =...
  26. H

    Mind blown by mechanical systems (2nd order)

    Homework Statement B, K, M Homework Equations 1. xs(t) -----spring ----mass-----damper-----fixed, derive DE for x of mass given :2. F - > M -----spring-------damper ---- fixed in series, derive the DE for velocity of spring The Attempt at a Solution 1. ma = -k(x-xs) -...
  27. E

    2nd order initial value problem in matlab

    Homework Statement 1.)I want to write a function in MATLAB that contains the 2nd order function: 20*d^{2}x;(dt^{2})+5*dx/dt + 20*x=0 (dampened spring) -The function should have 2 inputs (time,[initial values]) initial values should be a vector of 2 values -The function should...
  28. M

    Engineering Transfer Function Of A 2nd Order Circuit

    I'm trying to work out the Transfer function for the 2nd order RC circuit in the attachment below: I can't seem to get the right answer :( circuit: My answer: Please see attachment for my attempt and the relevant information:
  29. A

    Solving 2nd Order Linear DE with Constant Coefficients

    Hi, When solving a 2nd order Linear DE with constant coefficients (ay''+by'+cy=0) we are told to look for solutions of the form y=e^{rt} and then the solution (if we have 2 distinct roots of the characteristic) is given by y(t)=c_1 e^{r_1 t}+c_2 e^{r_2 t} This is clearly a solution, but...
  30. Z

    2nd order characteristic equation standart form

    A second order system has the following standart form; http://controls-design.com/mathtex/mathtex.cgi?H%28s%29%3DK%5Cfrac%7B%5Comega_n%5E2%7D%7Bs%5E2%2B2%5Czeta%5Comega_n%20s%2B%5Comega_n%5E2%7D%20%5Cmbox%7B%20for%20%7D%200%20%5Cle%20%5Czeta%20%5Cle%201 However, sometimes the system I...
  31. G

    Solving system of 2nd order coupled ODEs

    I have to derive equations of motion from Lagrangian and stumbled upon the following system of equations (constants are simplified, that information is unneeded) \begin{cases} \ddot{x}-A\dot{y}+Bx=0 \\ \ddot{y}+A\dot{x}+Dy=0 \end{cases} This is an extension of a simpler problem where B=D...
  32. T

    2nd Order difference eqn ZIR ZSR

    Homework Statement I have the following difference equation; y[n] -1.7y[n-1] -0.72y[n-2]=x[n] with aux conditions; y[-1]=1, y[-2]=-2 input; x[n] = (0.7)^{n}u[n] I used the recursive method to get 5 consecutive values of the impulse response of the system and also 5 consecutive values of...
  33. A

    Strange way of solving a linear 2nd order DE

    Homework Statement I was given a DE of the form: \Phi^{''}+(6/\eta)\Phi^{'}=0 where the next step was given as \Phi^{'} \propto \eta^{-6} where the answer came out to be \Phi \propto \eta^{-5} + constant The Attempt at a Solution My attempt was to set \Phi^{'}=x where I would then get...
  34. T

    Solving 2nd order differential

    Homework Statement I have to determine the 2nd,3rd and 4th derivative at 0. So ψ''(0) The equation is y'' + sin(x)y' + cos(x)y = 0 A know solution is y = ψ(x). The intial conditions are y(0) = 0 , y'(0) = 1 Homework Equations The Attempt at a Solution I know this is a...
  35. L

    Many body 2nd order energy shift of ground state

    This is more of a math question I suppose, but its in the context of calculating the second order energy shift in the ground state energy for a non relativistic collection of electrons. We end up showing that the energy shift has a finite and divergent piece. The divergent bit is proportional...
  36. W

    2nd order ODE - Show solution by substitution

    Homework Statement Show that y(t) = (1/w) ∫[0,t] f(s)*sin(w(t-s)) ds is a particular solution to y'' +w2 y = f(t)where w is a constant. The Attempt at a Solution After wasting several pages of paper I have made virtually no progress. Obviously, substitution suggests you plug in y(t)...
  37. B

    1st order or 2nd order distribution

    Hi, I'm fitting a distribution to the starting times of the first car journey in the day. I have a sample of 3,000 journey starting times. I am assuming that this sample represents the population well. I'm fitting a non parametric distribution. But my question is, should I fit a 1st...
  38. T

    Solving a 2nd order differential with fixed constant

    The question is to solve the equation y'' + ω^2y = cos(ωt) I know you'll find the complementary and particular functions and add them together. Now I found the complementary function easily. r= +/- ωi and then plug into the general equation for complex numbers. The problem I have is...
  39. ElijahRockers

    How to Solve a 2nd Order Non-Homogeneous DE with Repeated Roots?

    Homework Statement 4y''+4y'+y = cos(2t), y(0)=0, y'(0)=0 Homework Equations y(t)=yh+yp The Attempt at a Solution characteristic roots are repeated, m=-1/2, so y_h = A_1 e^{\frac{-t}{2}}+A_2 te^{\frac{-t}{2}} undetermined coefficients: yp = Acos(2t)+Bsin(2t) plugging into original...
  40. M

    General Solution of 2nd Order Differential Equaiton

    Homework Statement Find the general solution to d2y/dx2 +4y=cos(2x) Homework Equations The Attempt at a Solution I have woked out what I think is the Complementary function C1sin(2x)+C2cos(2x) the reason it is cos and sin is because the roots are 2i and therefore the exponential...
  41. M

    Two Variable 2nd Order Taylor Series Approximation

    Homework Statement Derive the Derive the two variable second order Taylor series approximation, below, to f(x,y) = x^3 + y^3 – 7xy centred at (a,b) = (6,‐4) f(x,y) ≈ Q(x,y) = f(a,b) + \frac{∂f}{∂x}| (x-a) + \frac{∂f}{∂x}|(y-b) + \frac{1}{2!}[\frac{∂^2f}{∂x^2}| (x-a)^2 + 2\frac{∂^2f}{∂x∂y}\...
  42. T

    Finding a fundamental set of solutions for a 2nd order differential equation

    Homework Statement 64y''+144y'=0 y1(0)=1 y'1(0)=0 and y2(0)=0 and y'2(0)=1 Homework Equations y1=c1*e^(r1*t) + c2*e^(r2*t)The Attempt at a Solution I start by finding the characteristic equation: 64r^2+144r=0 r1=-9/4 and r2=0 y1=c1e(r1*t) + c2e(r2*t) so I get y1=c1e^(-9/4 *t) + c2e^(0*t)...
  43. P

    Back Euler method for 2nd order d.e

    Hi, How can one use back Euler method for 2nd order d.e? Is it possible this method to be expanded for a system of 4 odes? Thanks
  44. L

    2nd order Differential Eq. - Reduction of Order

    I have a problem with differential equations - 2nd order - reduction of order my problem is as follows: (x − 1)y" − xy' + y = 0 , x > 1 ; y_1(x) = e^x solving this type of diff. eq. says to use y=y_1(x)V(x) which gives me y=Ve^x differentiating y gives me y'=V'e^x & y''=V''e^x...
  45. L

    2nd order homogeneous diff eq

    Homework Statement y"-2y'+5=0, y(∏/2)=0, y'(∏/2)=2 find general solution of this diff eq Homework Equations The Attempt at a Solution i have followed all of the steps for this, rather easy 2nd order diff eq, but i my solution differs from the books solution. steps...
  46. V

    What exactly is a 2nd order differential equation?

    A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change? Also, can anyone explain any application of...
  47. O

    Orbit of satellite 2nd order ODE using Matlab

    Hi, I am completely stuck on this problem that has been given to us. I must solve a set of 2nd order differential equations using Euler's method. It is for a geosychronous orbit of a satellite, meaning the orbit is circular and the velocity vector is perpendicular to the radius vector...
  48. K

    Separation of variables on 2nd order ode

    Hi all Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this? Also y'' =0. Is the same as. y''dx =0 dx Why is this legal?Thanks in advance
  49. M

    Solution to 2nd order ODE using the D operator method with 2 trig terms on RHS

    Hey, I have the DE y'' -2y' + 3y = xsin(x) + 2cosh(2x) Using the D operator as D = \frac{dy}{dx} this becomes (D2 -2D +3)y = xsin(x) + 2cosh(2x) so yp = \frac{1}{p(D^2)} operating on xsin(x) + 2cosh(2x) (i think) So i know if this was say \frac{1}{p(D^2)} operating on...
  50. B

    2nd order non-linear homogeneous differential equation

    Homework Statement Find a solution (Z2) of: z'' + 2z - 6(tanh(t))2z = 0 that is linearly independent of Z1 = sech2Homework Equations The Attempt at a Solution reduction of order gives you v''(t)(Z1(t))+v'(t)(2 * Z1'(t)) + v(t)(Z1''(t)+p(t)Z1'(t)) = 0 however the third term on the LHS can be...
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