Apply initial data and an inverse-square gradient law

(a) Solve $\cos^2x\,dy/dx=1$ for $0<x<\pi/2$, given $y=0$ when $x=\pi/4$, expressing y as a function of x.

(b) Find the equation of a curve through $(1,2)$ and $(1/4,-10)$ whose gradient is inversely proportional to $x^2$.