Converting second order ODE's to First Order

[Tygra_1983]

Hi Guys,

I have a basic understanding of converting second order ODE's to first order ODE's when you have for example, y'' + y' + y. However, I am stuck if you have a differential equation with just y''. For example, y'' = -f(L-x). How would I convert this equation into a set of first order ODE's?

Many thanks in advance

 

[Tygra_1983]

Anyone?

 

[3DDave]

Not a lot of mathematicians here. Does this help:

https://www.youtube.com/watch?v=l_YND1hSUmY

 

[Tygra_1983]

Again that is of the form y'' + y' + y. Thanks anyway.

 

[3DDave]

Yes - so do it with the coefficient of y' = 0.

 

[Tygra_1983]

Sorry 3DDave, could you explain further on that?

 

[3DDave]

y'' + 0*y' + a*y ...

 

[Tygra_1983]

Why is it no 0*y instead of a*y, as there is also no y variable?

 

[3DDave]

I'm guessing there is no solution. I see no references to that case.

You should be able to integrate twice.

 

[HTURKAK]

Double integration is the way..

When you write differential equation and search, one of the outcomes , the following web site ..

https://mathdf.com/dif/

Write your D.E. y'' = -f(L-x) , the solution is the following pdf . doc.