How to Solve an ODE with Mirror Functions?

[FrankST]

Guys,

I have an ODE like this:

The following code was used to generate this LaTeX image:


$$<br /> \frac{d^2y_{1}}{dx^2} + \frac{d^2y_{2}}{dx^2} + y_{1} + y_{2} = 0<br />$$


where, y1 (x) =y2 (-x).

Do you have any idea how to solve it?


Thanks in advance.

 

[Some Pig]

Let u(x)=y1(x)+y2(x), u"(x)=y1"(x)+y2"(x)
y1"(x)+y2"(x)+y1(x)+y2(x)=0
u"(x)+u(x)=0
u(x)=ae^ix+ae^-ix=y1(x)+y1(-x)
y1(x)=ae^ix+b
y2(x)=ae^-ix-b

 

[FrankST]

Thanks a lot.