Solve the differential equation, `(a^(2))/(xy).(dx)/(dy)=(x)/(y)+(y)/(x)-2,` is

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

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

The differential equation x(dy)/(dx)+(3)/((dy)/(dx))=y^(2)

Show that the differential equation x cos ((y)/(x))(dy)/(dx) = y cos ((y)/(x)) + x is homogeneous and solve it.

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

Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](dx)/(dy) = 1(x 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 solution of differential equation xdy(y^(2)e^(xy)+e^(x//y))=ydx(e^(x//y)-y^(2)e^(xy)), is

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