The general solution for the second order differential equation
\(\frac{d^2 y}{d x^2}-y=x \sin x\)
will be
(where C1 and C2 are arbitrary constants)
1
\(C_1 e^x+C_2 e^{-x}-\frac{1}{2}(x \sin x+\cos x)\)
2
\(C_1 e^x+C_2 e^{-x}-\frac{1}{2}(\sin x-x \cos x)\)
3
\(C_1 e^x+C_2 e^{-x}+\frac{1}{2} x(\sin x-\cos x)\)
4
\(C_1 e^x+C_2 e^{-x}+\frac{1}{2} x(\sin x+\cos x)\)