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

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

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

**
asked 2016-09-06 03:29:59 +0200 **

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

0

**
answered 2016-09-06 19:08:22 +0200 **

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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 :(

0

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)

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Asked: ** 2016-09-06 03:29:59 +0200 **

Seen: **394 times**

Last updated: **Sep 06 '16**

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