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

Answer

` y*logx=(-2/x)(1+logx) +c`

Explanation

We are given

`xlogx(dy)/(dx)+y=2/xlogx`


`(dy)/(dx)+(1/xlogx)y=2/(x^2)-(1)`


this is of the form `(dy)/(dx)+Py=Q`

here `P=1/(xlogx)` and `Q=2/(x^2)`


`therefore` I.F.`=e^(int Pdx)=e^(int 1/(xlogx) dx)`


`[`let `log x=t rArr 1/xdx=dt]`
`=int e^(1/t)=e^(logt)=t=logx`


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