Solve the following differential equation: `y\ dx+xlog(y/x)dy=2x\ dy`

Explanation

We have,



`y d x+{x log (frac{y}{x})} d y-2 x d y=0`


`Rightarrow{2 x-x log (frac{y}{x})} d y=y d x `


`Rightarrow frac{d y}{d x}=frac{y}{2 x-x log (frac{y}{x})}`



This is a homogenoeus differential equation.


Putting `y=v x` and `frac{d y}{d x}=v+x frac{d v}{d x}`, we get


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