# An ODE problem

Juggler123
Hi all,

I have an ODE of the form

$\frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0,$

where $\psi=C_{1}U(\xi)+C_{2}V(\xi).$

Is there any transformation or inventive manipulation I can use here to obtain an ODE for $\sigma=U(\xi)+V(\xi)$? As this is the quantity I would like to solve for.

Thanks.