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The first integral of (dy)/(dx)((d^2y)/(...

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

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

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

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

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

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

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

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

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

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

x^(2)((dy)/(dx))^(2)+xy(dy)/(dx)-6y^(2)=0