# How to solve ODE y'' - 4y' + y - x = 0 using rk4?

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How to solve ODE y''+y''-4y'+x = 0 using rk4?

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This looks like homework. If you want some help, you should ask more precise questions related to your research in solving those exercises, especially where you are locked.

( 2016-09-06 09:32:07 +0200 )edit

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This post is a wiki. Anyone with karma >750 is welcome to improve it.

I tryed

 # w = y''
# z = y'

var('x, w, z')

desolve_system_rk4( [w , 4*z + x] , [w,z] , ics = [0,1,0], ivar = x, end_points = 10, step = 0.1)


But does no work correty :(

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I got a way to solve the differential equation. If wrong please correct;)

To solve this differential equation we must first make a variable substitution to reduce the differential equation for a first order and thus create a system of ODEs. variable change:

w1 = y w2 = y w3 = y '

Thus, deriving the above variables, we have a system of equations of the form:

w1 '= w2 w2 '= f (x, w1, w2) = 4 * w2 + x

desolve_system_rk4([w2, 4*w2 + x ],[w1 , w2], ics = [0,1,0],ivar = x, step = 0.1, end_points = 2)

( 2016-09-06 23:18:07 +0200 )edit