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

Explanation

Given `x d y / d x+y=x log x` …………………… (i)


`d y / d x+y / x=log x`


This is linear differential equation


Integrating factor I.F. `=e^{int frac{1}{x} d x}=e^{log _{e} x}=x`


Multiplying both sides of (i) by
I.F. `=x`, we get


``
`x frac{d y}{d x}+y=x log x`


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