## anonymous 5 years ago Looking for the solution to equations of the form y''+y=0

1. anonymous

sinx, cosx?

2. anonymous

If y'' is proceded by a constant?

3. anonymous

y=Csinx and y=Ccosx......anybody?

4. anonymous

There is an e^ax factor before the trig functions, where a is a root of the characteristic equation. Should be something like y = ce^ax sinx + ce^ax cosx.

5. anonymous

That rings a bell, happen to know of a good tutorial/reference?

6. anonymous
7. anonymous

hope that helps.

8. anonymous

Great stuff, cheers matey.

9. anonymous

cheers

10. anonymous

this is the generic equation, but since $y=e^{ax}[C_{1}\cos(x)+C_{2}\sin(x)]\rightarrow a=0$ this will be you final equation $y=C_{1}\cos(x)+C_{2}\sin(x)$