I have a second-order nonhomogeneous linear differential equation, and its solution satisfies: \begin{alignat}{10} y(1)&{}={}& c_1x^2 & & &{}+{}& c*\cos x\\ y(2)&{}={}& c_2x^2 &{}-{}& c_3x &{}+{}& c*\cos x\\ y(3)&{}={}& x^2 &{}-{}& c_4x &{}+{}& c*\cos x \end{alignat} What is the set of fundamental solution for this kind of differential equation?
I think the fundamental set of solutions is: $\{x^2-x,\cos x\}$.
