Solve the following differential equation: `sqrt(1+x^2+y^2+x^2\ y^2)\ +x y(dy)/(dx)=0`

Solve the differential equation (tan^(-1)y - x)dy = ( 1 + y^(2))dx .

Solve the differential equation (dy)/(dx)=(x+2y-1)/(x+2y+1).

Solve the differential equation (dy)/(dx)=(2y-6x-4)/(y-3x+3).

Solve the differential equation y e^(x/y) dx = (x e^(x/y) + y^(2))dy ( y ne 0) .

Verify that the function y = e^(-3x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0

The order of the differential equation 2x^(2) (d^(2)y)/(dx^(2))-3(dy)/(dx) + y = 0 is

Solve the differential equation (x dy - y dx) y sin ((y)/(x)) = (y dx + x dy) x cos ((y)/(x)) .

Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](dx)/(dy) = 1(x ne 0) .