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(a) verfiy that y=tan(x+c) ia a one parameter family of solutions of the differential equation y'=...

(a) verfiy that y=tan(x+c) ia a one parameter family of solutions of the differential equation y'= 1+x^2

(b)since f(x,y)= 1+y^2 and df/dy= 2y are continuous everywhere, the region R can be taken to be the entire xy-plane. Use the family of solutions in part A to find an explicit solution of the first order initial value problem y'= 1+y^2, y(0)=0. Even though x0=0 is in the interval (-2,2) explain why the solution is not defined on its interval

(c)determine the largest interval I of the definition for the solution of the initial value problem in part b

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