Write down all solutions to the following boundary value problems. Label your answer as (i) unique solution, (ii) no solution, (iii) infinitely many solutions.
(a) $u^{\prime \prime}+2 u=2 x, u(0)=0, u(\pi)=0$,
(b) $u^{\prime \prime}+4 u=\cos x, u(-\pi)=0, u(\pi)=1$,
(c) $u^{\prime \prime}-2 u^{\prime}+u=x-2, u(0)=-1, u(1)=1$,
(d) $u^{\prime \prime}+2 u^{\prime}+2 u=1, u(0)=\frac{1}{2}, u(\pi)=\frac{1}{2}$,
(e) $u^{\prime \prime}-3 u^{\prime}+2 u=4 x, u(0)=0, u(1)=0$,
(f) $x^2 u^{\prime \prime}+x u^{\prime}-u=0, u(0)=1, u(1)=0$,
(g) $x^2 u^{\prime \prime}-6 u=0, u(1)=1, u(2)=-1$,
(h) $x^2 u^{\prime \prime}-2 x u^{\prime}+2 u=0, u(0)=0, u(1)=1$.