Question

How do you solve the IVP, y' = y^2 + 2, y(0) = 1

Answer 1

It's separable so you have dy/dx=y^2+2. You want to get all the y's together with the dy. So multiple both sides by dx. Then divide both sides by y^2+2. You have
1/(y^2+2)dy=dx. Integrate both sides and plug in initial conditions to solve for the constant of integration