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

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.

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

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

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

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

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

The straight line y=2x meets y=f(x) at P, where f(x) is a solution of the differential equation (dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2)) such that f(1)=3 , then f'(x) at point P is

If the straight line y=x meets y=f(x) at P, where f(x) is a solution of the differential equation (dy)/(dx)=(x^(2)+xy)/(x^(2)+y^(2)) such that f(1)=3 , then the value of f'(x) at the point P is

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