integrate dy/dx=x(y^(1/2))(cos^2(y^(1/2))^2)

Question

I know I need to separate, and Iv'e moved dx to the right side with dy on the left. Don't know how to go on.

Answer 1

let z = y^.5
then dz = .5 y^-.5 dy
dy = 2 y^.5 dz = 2 z dz

2 z dz /(z cos^2 (z) ) = x dx

dz/( cos^2 (z)) = .5 x dx

tan z = .25 x^2 + constant
tan y^.5 = .25 x^2 + constant