Chapter 6.1, Problem 8E

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

has a solution $y=\tanh (t+c)$.