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(xy - x^(2))dy/dx = y^(2)...

`(xy - x^(2))dy/dx = y^(2)`

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

x^(2)(dy)/(dx)+y^(2)=xy

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

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

The solutio of the differential equation (x^(2)-xy^(2))(dy)/(dx)+y^(2)+xy^(2) = 0 is

y^(2)-x^(2) (dy)/(dx) = xy(dy)/(dx)

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be

If y=x^(x) ,then xy (d^(2)y)/(dx^(2))-x((dy)/(dx) )^(2)=

xy (dy)/(dx) =x^(2) +2y^(2)

Solve (x^(2) + y^(2))(dy)/(dx) = 2xy