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

If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =

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

The solution of the differential equation (dy)/(dx)=(xy)/(x^(2)+y^(2)) is

Find the particular solution of eh differential equation (dy)/(dx)=(xy)/(x^(2)+y^(2)) given that y=1 when x=0.

STATEMENT -1 : The differential equation (dy)/(dx) = (2xy)/(x^(2) + y^(2)) Can't be solved by the substitution x = vy. and STATEMENT-2 : When the differential equation is homogeneous of first order and first degree, then the substitution that solves the equation is y = vx.

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

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

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