a) Solve the differential equation (x+1) \frac{\mathrm{d} y}{\mathrm{~d} x}+x=1 \quad(x>0) b) Use separation of variables to find the solution to the differential equation \frac{\mathrm{d} y}{\mathrm{~d} x}+\sin ^{2} y=1 O when

x1. Write your solutionthat satisfies the boundary condition yin explicit form for y.%3D (c) Use an integrating factor to find the general solution to the linear differentialequation x^{2} \frac{\mathrm{d} y}{\mathrm{~d} x}-x y=1 \quad(x>0)