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

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

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

Consider the homogeneous differential equation (dy)/(dx)=f((y)/(x)) By putting (y)/(x)=v , the equation reduces to (dv)/(f(v)-v)=(dx)/(x) . Integrating we get int(dv)/(f(v)-v)=int(dx)/(x)+c Solution of x(x-y)dy+y^(2)dx=0 is-

(x-y)dy-(x+y)dx=0

Solve: x(x-y) dy + y^(2) dx= 0

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

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

y dx-x dy+y^2cosx dx=0

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

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