**(a)** Find Wronskian $W(y_1,y_2)(x)$ of a fundamental set of solutions $y_1(x) , y_2(x)$ for ODE

\begin{equation*}

\bigl(x\sin(x)+\cos(x)\bigr)y''-x\cos(x)y'+\cos(x)y=0

\end{equation*}

**(b)** Check that $y_1(x)=x$ is a solution and find another linearly independent solution.

**(c)** Write the general solution, and find solution such that ${y(0)=1, y'(0)=1}$.