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Solve `xy(1+xy^2)(dy)/(dx)=1`
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`therefore(dx)/(dy)=xy+x^2y^3`
`therefore 1/x^2(dx)/(dy)-1/xy=y^3` Now, put`-1/x=v`
`therefore (dv)/(dy)+vy=y^3` ...........................``
This is linear differential eqn.
∴ Integrating Factor `=e^(intydy)=y^2/e^2`
The solution of linear diff. eqn is given by,
ЁЭТЧ.(I.F.) = ∫(ЁЭС░.ЁЭСн.)(ЁЭС╣.ЁЭСп.ЁЭС║) + c
`ve^(y^2/2)=inte^(y^2/2)(y^2-2)+c`
Where c is constant of integration.
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The general solution of \[x\left(x-1\right)\frac{\mathrm{d}y}{\mathrm{d}x}=x^{3}\left(2x-1\right)+\left(x-2\right)y\mathrm{}\] is
