`x^(2)(dy)/(dx)+xy=4`

The equation of curve passing through origin and satisfying the differential equation (1+x^(2))(dy)/(dx)+2xy=4x^(2), is

(1-x^(2))(dy)/(dx)-xy=1

Solve (1+x^(2))(dy)/(dx)=xy

Solve: (1+x^(2))(dy)/(dx)+2xy-4x^(2)=0 subject to the initial condition y(0)=0

y^(2)-x^(2) (dy)/(dx) = xy(dy)/(dx)

(1-x^(2))(dy)/(dx)+xy=ax

(1-x^(2))(dy)/(dx)-2xy=x-x^(3)

(1-x^(2))(dy)/(dx)-xy=x^(2)

The solution of (1-x^(2))(dy)/(dx)+xy=5x

e^(-x^(2))(dy)/(dx)=2xy