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From: Franziska on 5 Feb 2010 03:02
Hi all

I have a differential equation similar to the following:
A-Bx(t)-Cx'(t)^2-Dx''(t)=E-Fy(t)-Gy'(t)^2-Hy''(t)

I want to use ODE-solver. But I am not sure about the step before:
How to convert it to a system of 4? differential equations of first order?

Z'(1)=x'(t)
Z'(2)=x''(t)=?
Z'(3)=y'(t)
Z'(4)=y''(t)=?

Would be very nice, if someone could give me some hints.

Cheers,
Franziska
From: Torsten Hennig on 4 Feb 2010 17:28
> Hi all
>
> I have a differential equation similar to the
> following:
> A-Bx(t)-Cx'(t)^2-Dx''(t)=E-Fy(t)-Gy'(t)^2-Hy''(t)
>
> I want to use ODE-solver. But I am not sure about the
> step before:
> How to convert it to a system of 4? differential
> equations of first order?
>
> Z'(1)=x'(t)
> Z'(2)=x''(t)=?
> Z'(3)=y'(t)
> Z'(4)=y''(t)=?
>
> Would be very nice, if someone could give me some
> hints.
>
> Cheers,
> Franziska

You have only one differential equation for two
unknown functions - it's not possible to solve it
as stated.

Best wishes
Torsten.
From: Franziska on 5 Feb 2010 03:34
"Franziska " wrote in message <hkgj9q$hq0$1(a)fred.mathworks.com>...
> Hi all
>
> I have a differential equation similar to the following:
> A-Bx(t)-Cx'(t)^2-Dx''(t)=E-Fy(t)-Gy'(t)^2-Hy''(t)
>
> I want to use ODE-solver. But I am not sure about the step before:
> How to convert it to a system of 4? differential equations of first order?
>
> Z'(1)=x'(t)
> Z'(2)=x''(t)=?
> Z'(3)=y'(t)
> Z'(4)=y''(t)=?
>
> Would be very nice, if someone could give me some hints.
>
> Cheers,
> Franziska

Sorry, the equation is even more complicated:
A-Bx(t)x'(t)-Cx'(t)^2-Dx(t)x''(t)=E-Fy(t)y'(t)-Gy'(t)^2-Hy(t)y''(t)
I can write it with matrices. But still I have terms with x(t)x''(t) for example.
Anyone, who could give me a hint?
From: Franziska on 5 Feb 2010 04:05
Thanks Torsten for your answer.

Acutally I have two equations (see below). But I thought I have to substitute equ (II) in (I) and then again only work with one equation.

I) A-Bx(t)x'(t)-Cx'(t)^2-Dx(t)x''(t)=E-Fy(t)y'(t)-Gy'(t)^2-Hy(t)y''(t)
II) Q=x'(t)*a+y'(t)*b

where A,B....,H,Q,a,b are constants.

So, now again: Is it now possible to transform these two equations to a system of first order equations?

Cheers,
Franziska
From: Franziska on 5 Feb 2010 04:05
Thanks Torsten for your answer.

Acutally I have two equations (see below). But I thought I have to substitute equ (II) in (I) and then again only work with one equation.

I) A-Bx(t)x'(t)-Cx'(t)^2-Dx(t)x''(t)=E-Fy(t)y'(t)-Gy'(t)^2-Hy(t)y''(t)
II) Q=x'(t)*a+y'(t)*b

where A,B....,H,Q,a,b are constants.

So, now again: Is it now possible to transform these two equations to a system of first order equations?

Cheers,
Franziska
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