Calculus
posted by Mina .
Solve the firstorder initial value problem using half angle formulas
{y'(x)= 1 + sin^2 x
y (0)= 7

use the identity
cos 2x = 1  2sin^2 x
and solving for sin^2 x
sin^2 x = 1/2  (1/2)cos 2x
then y'(x)= 1 + sin^2 x
becomes
y'(x)= 1 + sin^2 x
becomes
y'(x)= 1 + 1/2  (1/2)cos 2x
= 3/2  (1/2)cos 2x
this is now easy to integrate
Don't forget to add the constant.
plug in the point (0,7) to find that constant.