Let $\lambda$ be a real number , $(c_k)$ a complex sequence with $\mid c_k \mid \leq C(1+\mid k \mid)^{-2}$ for all k with a constant $C \geq 0 $. Find all periodic, two times differentiable functions $f:R -> R$ which fulfil the differential equation
\begin{equation*}
f''-\lambda f'+f=\sum_{k=-\infty}^\infty c_ke^{ikx}.
\end{equation*}
I already solved the homogenous equation with
\begin{equation*}
f(x)= c_1 e^{1/2 (\lambda-\sqrt{\lambda^2-4} )x}+c_2 e^{1/2(\lambda+\sqrt{\lambda^2-4})x}
\end{equation*}
sadly thats as far as I come. Can someone help me out on this one?
2026-04-01 13:30:50.1775050250
Solving differential equation with Fourier-series-inhomogenity
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