2nd order Definition and 494 Threads

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  1. P

    Solving 2nd Order Non-Homogeneous DE with Variables: A Comprehensive Guide

    I am familiar with how to solve a second order, non-homogenous DE with constants, i.e. \frac {\partial^2X(t)}{\partial t^2} + \frac{\partial X(t)}{\partial t} = C by first solving the homogenous eqn, then setting the equation equal to a constant, yielding a sol'n of X(t)= Ae^{0}+...
  2. D

    How to Solve a Second Order Differential Equation with Given Initial Conditions?

    Ok, so i tried to solve this problem: Find y as a function of t if: 100Y"-729y=0; y(0)=6, y'(0)=1 this is what i did so far: 100r^2-729r=0 r(100r-729)=0 r=0, r=729/100 y(x)=C1+C2*e^((729/100)*t) y'(x)=C1+729/100C2*e^((729/100)t) am I on the correct track? After I substitute the...
  3. Z

    Finding the Constant for Solving a 2nd Order Differential Equation

    can any1 help me solve this? d2x/dt2 = -(k/m)*x -g at x= 0, t=0, v=sqrt(u^2-2gh) what is x?? can show the steps?
  4. H

    Power series to solve 2nd order ordinary differential equations

    I need some help with power series. I can't remember how to find a power series center around a point. example question: y"-xy'-y=0, x=1 I don't how to start this.
  5. A

    Can You Solve a 2nd Order Non-Homogeneous DE with Varying Coefficients?

    Does anyone know how to solve this? \frac {d^2V(t)}{dt^2} + \frac{V(t)}{w} = \frac{Vm}{w}
  6. A

    MATLAB How Do You Solve a 2nd Order ODE Using Matlab?

    Dear All, I have a Problem about a 2nd order ode. I don't know how it can be solved with Matlab. If someone know about it then please let me know. I need to get the values of x & y. All other values are known. The equation is: [ M + mf mf mf mf ][ ¨x ¨y...
  7. D

    Non-homogeneous 2nd order diff eq involves power series

    I just need a hint or something to see where I start. I'm at a loss for a beginning. Consider the non-homogenous equation y'' + xy' + y = x^2 +2x +1 Find the power series solution about x=0 of the equation and express your answer in the form: y=a_0 y_1 + a_1 y_2 + y_p where a_0 and...
  8. D

    Non-Homogenous Power series 2nd order equation

    I just need a hint or something to see where I start. I'm at a loss for a beginning. Consider the non-homogenous equation y'' + xy' + y = x^2 +2x +1 Find the power series solution about x=0 of the equation and express your answer in the form: y=a_0 y_1 + a_1 y_2 + y_p where a_0 and...
  9. G

    How can I improve my solution for this 2nd Order D.E.?

    I'm have a lot of trouble trying to find the general solution to the following D.E. y'' + 6.4y' + 10.24y = e^(-3.2x) I get the homogeneous solution as C1*e^(-3.2x)+C2*x*e^(-3.2x) and the particular solution as 0 So a general solution of Y=C1*e^(-3.2x)+C2*x*e^(-3.2x) I know my solution is...
  10. K

    Eigenvalue Method: Solving 2nd Order ODEs

    Given:Second order ODE: x" + 2x' + 3x = 0 Find: a) Write equation as first order ODE b) Apply eigenvalue method to find general soln Solution: Part a, is easy a) y' = -2y - 3x now, how do I do part b? Do I solve it as a [1x2] matrix?
  11. Z

    2nd order homogenous differential equation

    Solve the following for y(x); y'' - 3y' + 2y = 0 I kind of know what to do up to a point but after that I`m stuck (bad notes and no textbook!). Here`s what i`ve done so far, if someone could hint as how to finish this question i should be able to do the other 9 I have. let y =...
  12. M

    Confused on how my professor did this last step, DiffEQ, 2nd OrdER

    Hello everyone! My professor was going over a problem real fast for the exam and now that i went over it again, I'm lost on how he did this last step. He is using a method called Abels Theorum. THe problem says: Find a second solution of the given differential equation: t^2y''+3ty' + y = 0...
  13. M

    Confused what method to use on this Diff EQ 2nd order

    ello ello! I havn't seen an example of this type of problem. It has another variabler in the equation, i tried to divide by it, but its still in there. Here is the problem: Find y as a function of x if...
  14. M

    Can i apply the same technique as I did with real solutions? D.E. 2nd order

    Hello everyone! I had a question, I solved a problem very similar to this one but it has 2 real soltions which took the form of: y (x) = Ae^rx + Be^(rx) But now i have repeated roots: y(x) = e^(rx)*(A + Bx); HEre is the problem: Find y as a function of x if x^2 y'' - 11 x y' + 36 y =...
  15. M

    2nd order Diff EQ with x^2*y'', what shall i do i missed it

    Hello everyone! i'm confused on how to approach this problem, my professor did an example and he used m^2-m-4m+6 = 0, if u have t^2*y''-4ty' +6y = 0; So i tried to do the following, but the answer is wrong. Anyone see? http://img88.imageshack.us/img88/3603/lastscan7jj.jpg THanks!
  16. M

    What happens if you only get 1 solution to a 2nd Order Diff EQ?

    Hello everyone, I'm slightly confused on this problem, when i factored it and solved for r, i came out with only 1 answer, r = -13/72 Here is my problem and work: http://img213.imageshack.us/img213/685/lastscan15uk.jpg :biggrin:
  17. M

    2nd Order Diff EQ with 2 intial conditions, got complex roots, i f'ed it up

    OKay i havn't gotten 1 2nd order Diff EQ right yet! I'm on a role! wee! Find y as a function of t if 81y'' + 126y' + 79y = 0, y(0) = 2, y'(0) = 9 . Here is my work: http://img204.imageshack.us/img204/4605/lastscan5ag.jpg I submitted this and it was wrong...
  18. M

    Confused on why i'm missing this 2nd Order Diff EQ with complex roots

    Hello everyone. I"m not getting this problem right. <insert sad face here> Find y as a function of t if 6y'' + 33y = 0, y(0) = 8, y'(0) = 5 . y(t) = hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11...
  19. M

    Simple homogenous 2nd order Diff EQ, but i'm stuck on the process

    Hello everyone, we just started 2nd order differentials, and i was loooking at his example and it made senes but now I'm doing the homework and I'm stuck. Here is the problem: Find y as a function of t if y'' - 3y' = 0, y(0) = 9, y(1) = 7 . y(t) =? Well there is my work...
  20. B

    Help with 2nd order differential equations needed

    I have come across the following question when revising for my upcoming exam, and wondered if anyone wouldn't mind giving me a hand and some hints as how to solve it. So far I have: F_{m} - k\frac{ds}{dt} = m\frac{d^2s}{dt^2} And now I'm stuck as to the solution of the equation, as its...
  21. B

    1st order, 2nd order Rate reactions HELP

    1st order, 2nd order Rate reactions HELP! I have read the section of my book over and over and studied the practice problems, but I still do not understand 1st order, 2nd order, or 0 order rate reactions. What does it mean to be of any particular order?
  22. A

    What went wrong with my calculations for a 2nd order D.E. solution?

    for the following question: y``+y`+9.25y=2+2x+x^2 my problem: yh=c1+c2e^(-x) suppose yp=c3x^2 + c4x+c5 then yp`=2c3x+c4 so yp``=2c3 then 2c3+2c3x+c4=2+2X+X^2 so c3=1, c4=1 so yp=x^2+x then y=c1+c2e^(-x)+x^2+x which implies c1=8 => y=8+c2e^(-x)+x^2+x so y`=-c2e^(-x)+2x+1...
  23. Z

    Numerical solution of 2nd order ODE

    Got this problem and we've been given a program which can solve for x, for the equation: Ax = b Where A = \left( \begin{array}{rrrrrr} b & c & 0 & 0 & \cdots & 0 \\ a & b & c & 0 & \cdots & 0\\ 0 & \ddots & \ddots & \ddots & & \vdots \\ \vdots & & \ddots & \ddots & \ddots & 0 \\ \vdots & & &...
  24. B

    Solving a 2nd Order ODE Using Series

    Hi, can someone help me with the following question? I need to solve the ODE using series. y'' + 4y' + 3y = 0 Firstly, using the characteristic equation I know the general solution is of the form y\left( x \right) = Ae^{ - x} + Be^{ - 3x} . So I know roughly what I should get...
  25. S

    H value in runge kutta method 2nd order

    hi can anyone explain to me how to get the H value for runge kutta second method? I've searched everywhere online but i just don't understand it. if found h = tn - to/n?? i know what value of "to" is but no clue what values to put in for n and tn? thanks
  26. A

    Solving 2nd Order ODE: yy``=2y`^2

    for the following question: yy``=2y`^2 my problem: i don't have a clue how to get a hand on this one! any suggestions?
  27. V

    DiffEQ 2nd order series sol'n problem: (1 - x)y'' + y = 0, x0 = 0

    This problem is from section 5.2 in Boyce, DiPrima's Differential Equations 8th edition. (1 - x)\,y''\,+\,y\,=\,0 I get: 2\,a_2\,+\,a_0\,+\,\sum_{n\,=\,1}^{\infty}\,\left[(n\,+\,2)\,(n\,+\,1)\,a_{n\,+\,2}\,-\,n\,(n\,+\,1)\,a_{n\,+\,1}\,+\,a_n\right]\,x_n\,=\,0 Which leads to one...
  28. V

    Diff. EQ: How do I solve a 2nd order linear EQ with series?

    This is problem number 1 (yes, one) in chapter 5.2 in Boyce, DiPrima, 8th edition. y'' - y = 0, x_0 = 0 Substituting the series for y and y-double prime: \sum_{n = 2}^{\infty} n (n - 1) a_n x^{n - 2} - \sum_{n = 0}^{\infty} a_n x^n = 0 Now, substituting n + 2 for n in first term...
  29. R

    Problem in Newtonian gravity- 2nd order, integration problems

    The problem is this: Given sun of mass M and a body of mass m (M>>m) a distance r from the sun, find the time for the body to 'fall' into the sun (initially ignoring the radius of the sun). Our first equation is therefore \frac {d^2r}{dt^2} = \ddot{r} = \frac {GM}{r^2} . I am able to...
  30. E

    Source-free 2nd order lin. circuit

    RLC second order linear network question: So, we are given this equation which is the same for Vc(t) and iL(t) expressed as x(t): 2nd deriv of x(t) + R/L(1st deriv of x(t)) + 1/(LC)(x(t)) = 0; And in one of the problems it asks to find both equation for the Vc(t) and iL(t) for t < 0, and...
  31. E

    Difference Quotient and 2nd Order PDEs

    I am trying to match a result in one of my textbooks. To assist with one of their arguments they are approximating a 2nd order PDE by using a difference quotient and they show the approximation as follows: (d^2u[x,t])/(dx^2) =~ (1/h^2)(u[x+h,t]-2u[x,t]+u[x-h,t]) When I actually use...
  32. S

    Solving Systems of 2nd Order DE's with Eigenvalues and Eigenvectors

    I have this DE and I do not know how to solve it. This is a problem in my review questions that my professor handed out, but we have never done a problem like this in class, so I do not know where to start. here is the problem: x'' = 4x - 5y y'' = 2x - 3 I need to solve it using...
  33. J

    Converting 2nd Order ODE to 1st Order ODE

    I'm stuck as to where to start with this question: The position function x(t) in a certain nonlinear system is described by the second order ODE: < equation.gif > Transform this ODE into a pair of first order ODEs for x1=x and x2=dx/dt. (Note that x2 represents the velocity in this...
  34. J

    Is My Technique Correct for Solving 2nd Order Nonlinear Differential Equations?

    this is the problem: xy'' -x(y')^2 = y' my book says that i need to substitute u=y' and du/dx=y''... so i get: x(du/dx)-xu^2 = u so next the book says i need to separate the x's/dx' to one side and u's/du's to the other. however, i cannot do it am i using the correct technique...
  35. J

    Need help with nonlinear 2nd order DE

    problem: xy'' -x(y')^2 = y' what i have so far: u=y' and du/dx=y'' du/dx - u^2 = (1/x)u int[(1/u)-u]du = int[1/x]dx ln u - (1/2)u^2 = ln x +c ok, now is what I've done so far correct? what do i do next? ps: i'd like to say hi to everyon :) I am new here
  36. Z

    Numerical resolution of 2nd order non-linear differential equation

    Hi Everybody, Does anybody know how to solve, analytically or numerically, the following differential equation : \frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2}) The unknown function is \Phi. a and b are some strictly positive constants. q\Phi is...
  37. cepheid

    General Solutions of 2nd Order Linear Homogeneous Ordinary D.E.s

    A theorem in my textbook is confusing me: For the functions p(t) \ \ \text{and} \ \ q(t) continuous on an open inteval I defined by \alpha < t < \beta : We have differential equation L[y] = 0 where L = (\frac{d^2}{dt^2} + p\frac{d}{dt} + q) The theorem attempts to prove...
  38. S

    Reducing 2nd order to 1st order type question

    Help! I'm just starting this class and I have no idea what's going on. What I don't understand is, what answer are you supposed to give? My question says "Find the general solution and also the singular solution, if it exists". What the hell does that mean? Can someone tell me if this...
  39. M

    Could use a little advice here, with a 2nd order ODE

    xy'' -(2x+1)y' + (x+1)y = (x ex)2 I know a solution - (x-1)e2x Thus, y= ((x-1)e2x u(x)) Now, i know how to do the whole reduction of order thing, but when i find y' and y'' and substitute, the u(x) term doesn't cancel out so this doesn't work (x2-x)u'' + (2x2-x+1)u' + x2u = x2 So...
  40. B

    How Do You Solve for Coefficients in a Power Series for a 2nd Order DE?

    After setting out in the sums and collecting the terms in x^j I'm left with a series of expressions in a_2, a_3 etc as I believe I'm supposed to. However my first expression reads 2a_{2}+2a_{1}+a_-_{1}=0 Now I'm told that y(o) = 1 and y'(o) = 0 I think this means that a_0 = 1 and...
  41. A

    2nd order DE, is there a way to solve this without series?

    It looks simple enough: y'' + x*y = x^2 However, I tried and I could not find a nontrivial solution to the homogeneous equation: y'' + x*y = 0 Am I right in thinking you need to solve this with series? No need to actually do it, I just need to know if it is possible otherwise...
  42. A

    Solving a 2nd Order Differential Equation with Auxiliary Method

    ok im trying to solve the following equation using standard aux method: d^2y/dx^2 + 3dy/dy +2y = cos x with conditions x(0)=-3 and x'(0) = 3 my aux eqn is: ae^x + be^-2x and my yp is; a sin kx + b cos kx i differentiate this twice and substitute into the original...
  43. P

    How do I solve a 2nd order DE with constants a, b, c1, and c2?

    hi all... i need to solve this differential equation of 2nd order...if anyone could tell me the way or method to use to do it i would appreciate it. i don't mind if the sol is given :wink: a*x^2 y''+(bx-c1)*y'-by+c2=0 where y'=dy/dx and y"=d^2y/d^2x a,b,c1,c2 are constants thanx
  44. A

    How Can We Solve the Unsolved 2nd Order Differential Equation?

    Hi, When I was younger, a teacher of mine gave me this problem for training: http://perso.wanadoo.fr/eric.chopin/pbX_en.htm This was a test for the admission to a well known french Engineering School. What was interesting was that the test contains a question that was unsolved...
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