Solving differential equation with initial condition

Question

dy/dx= (sec^2(x))/(1+y) , condition (0,2) 

 

I got y^2= 2(tanx-x) +C . Im not sure if this is right

Answer 1

(1+y) dy = sec^2(x)dx

 

left side

 

y + 1/2y^2 + C1

 

right side

 

tan(x) + C2

 

Therefore,

 

y + 1/2y^2 = tan(x) + C

 

2y + y^2 = 2tan(x) + C

 

plug in point

 

4 + 4 = C 

 

8 = C

 

2y + y^2 = 2tan(x) + 8