Calculus (3rd Edition)

$$y=\tan^{-1}(x+1) .$$
By separation of variables, we have $$\sec^2ydy= dx$$ then by integration, we get $$\tan y=x+c .$$ Now, since $y(0)=\pi/4$, then $c=1$. So the general solution is given by $$y=\tan^{-1}(x+1) .$$