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

Explanation

`x e^{\frac{y}{x}}-y+x \frac{d y}{d x}=0, y(e)=0`

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

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{v x-x e^{\frac{v x}{x}}}{x}`

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