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The general solution of the differential...

The general solution of the differential equation `(y^(2)-x^(3)) dx - xydy = 0(x ne 0)` is: (where c is a constant of integration)

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The correct Answer is:
5
`xy(dy)/(dx)=(y^(2)-x^(3))`
`y(dy)/(dx)-(y^(2))/x=-x^(2)`
`y^(2)=timplies2y (dy)/(dx)=(dt)/(dx)`
`2 (dt)/(dx)-t/x=-x^(2)implies(dt)/(dx)-2/xt=-2x^(2)`
IF`=e^(-int1/x dx)=e^(-2In(x))=1/(x^(2))`
`t/(x^(2))=int-2dx`
`t/(x^(2))=-2x+Cimpliesy^(2)=-2x^(3)+Cx^(2)`
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