Dy/dx=2xy/x²+y² solve​

Step-by-step explanation:

As it is first order nonlinear ordinary differential equation

Let y(x) = x v(x)

2xy/(x²+y²)=2v/(v^2+1)

dy=xdv+vdx

dy/dx=d(dv/dx)+v

x(dv/dx)+v=(2v)/(v^2+1)

dv/dx=[(2v)/(v^2+1)-v]/x

u=v^2

du=2vdv

Left hand side:

∫

=∫

=∫

=

=

Right hand side:

Solve for v:

i think the answer is b