`dy/dx = 2xy`

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

Solve dy/dx = xy + x + y + 1

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

Show that the differential equation x^(2)(dy)/(dx) = x^(2)+ xy + y^(2) is homogeneous differential equation. Also find its general solution.

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.

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

Find dy/dx if y= xy

Find dy/dx If xy= sinx

Find the value of dy/dx if xy=siny+cosy

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