Solve each of the following initial value problem: `(x y-y^2)dx+x^2dy=0,\ y(1)=1`

Explanation

`(x y-y^{2}) d x-x^{2} d y=0, y(1)=1`

`\frac{d y}{d x}=\frac{x y-y^{2}}{x^{2}`

It is a homogeneous equation

Put `y=v x`

And `x \frac{d v}{d x}+v=\frac{d y}{d x}`.

So,

`x \frac{d v}{d x}+v=\frac{x v x-v^{2} x^{2}}{x^{2}} `

`x \frac{d v}{d x}=v-v^{2}-v `

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