Question

Solve the following differential equation algebraically
dy/dx = xy^2 + 4x y(0) = 0

I reached the point dy/(y^2+4) = xdx but I don't know how to solve the left side of the equation.

Answer 1

dy/dx = xy^2 + 4x
dy/dx = x(y^2+4)
dy/(y^2+4) = x dx
now just integrate both sides.

Answer 2

1/2 arctan(y/2) = 1/2 x^2 + c/2
y/2 = tan(x^2 + c)
y = 2 tan(x^2+c)

Answer 3

I got that, but I wasn't sure how to integrate dy/(x^2+4)

Answer 4

sorry I responded too early, thank you so much