(1+x^(2))(dy)/(dx)+2xy-4x^(2)=0

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

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

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

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

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

If the solution of (1 + x^(2) )dy/dx + 2xy - 4 x^(2) = 0 is 3y(1+x^(2)) = kx^(3) + c, then the value of k is -

(1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2) , given that y = 0 , when x =0

Solve the differential equation (1 + x ^(2)) (dy)/(dx) = 4x ^(2) - 2xy