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

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

Solve :- (x^2+y^2)dx-2xy dy=0

Solve: (1-x^2)(dy)/(dx)-xy=x^2 , given y = 2 when x= 0.

Solve : (x+xy^(2))dx+(y+x^(2)y)dy=0

Solve : (x^(2)-y^(2)) dx + 2xy dy = 0

Solve: y^2dx+(xy+x^2)dy =0

Solve: y(2xy+1)dx+x(1+2xy+x^2y^2)dy=0

Solve the differential equation (d^2y)/(dx^2)=x+sinx subject to the condition that (dy)/(dx)=0 and y=0 when x=0 .