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.

Find the real value of m for which the substitution y=u^m will transform the differential equation 2x^4y(dy)/(dx)+y^4=4x^6 in to a homogeneous equation.

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

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

Solve the differential equation dx/dy​=xy+3x+y+3

Show that the differential equation 2ye^(x/y) dx + ( y - 2xe^(x/y)) dy = 0 is homogeneous and find its particular solution, given that, x = 0 when y = 1.

Solve the differential equation xy(dy)/(dx)=x^(2)-y^(2).

Show that the differential equation (x - y) (dy)/(dx) = x + 2y is homogeneous and solved it.

Differential equation y log y dx - x dy = 0

Show that the differential equation 2ye^(x/y)dx+(y-2xe^(x/y))dy=0 is homogeneous and find the particular solution, given that x=0 when y=1 .