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I have an ODE of the form

[itex]\frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0,[/itex]

where [itex]\psi=C_{1}U(\xi)+C_{2}V(\xi).[/itex]

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

Thanks.