Show that the differential equation `y^3dy+(x+y^2)dx=0` can be reduced to a homogeneous equation.

Show that the differential equation y^(3)dy-(x+y^(2))dx=0 can be reduced to a homogenous equation.

Solve the differential equation: y\ dx+(x-y^2)dy=0

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

Solve the differential equation (x y^2+x)dx+(y x^2+y)dy=0

Solve the differential equation: (x+3y^2)(dy)/(dx)=y

Solve the differential equation: 2x y \ dx+(x^2+2y^2)dy=0

Show that the differential equation (x e^((y)/(x)) + y) dx = x dy is homogeneous differential equation.

Solve the differential equation: (1+y+x^2y)dx+(x+x^3)dy=0

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

The substituion y=z^(alpha) transforms the differential equation (x^(2)y^(2)-1)dy+2xy^(3)dx=0 into a homogeneous differential equation for