Find the general solution of the differential equations: `xlogx(dx)/(dy)+y=2/xlogx`

Explanation

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`x log x frac{d y}{d x}+y=frac{2}{x} log x`

`Rightarrow frac{d y}{d x}+frac{1}{x log x} y=frac{2}{x^{2}}`

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This is a linear differential equation of the form

`frac{d y}{d x}+P y=Q`

when `P=frac{1}{x log x}` and `Q=frac{2}{x^{2}}`

`therefore quad` I.F `=e^{int {Pix}}=e^{int frac{1}{x log x} d x}`

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