Problem

(a) Use the substitution $u=1+x^2$ to find

$$\int\frac{x}{\sqrt{1+x^2}}\,\mathrm{d}x.$$

(b) Find the solution of the differential equation

$$x\frac{\mathrm{d}y}{\mathrm{d}x}-y=x^2\sinh^{-1}x,$$

given that $y=1$ when $x=1$. Give your answer in the form $y=f(x)$.