Chapter 6.1, Problem 7E

(a) Show that $y=\tan (t+c)$

is a solution of the differential equation $y\text{'}=1+y^2$ for each c. (b) For each real number $y_0$, find c in the interval $(-\pi /2,\pi /2)$ such that the initial value problem $y\text{'}=1+y^2$, $y(0)=y_0$, has a solution $y=\tan (t+c)$.