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

Explanation

`x(dy)/(dx)+2y=x^(2)logx`
`implies (dy)/(dx)+(2)/(x)y=x logx`
Here, `P=(2)/(x)`, `Q=x log x`
`:. I.F.=e^(intPdx)=e^(int(2)/(x)dx)`
`=e^(2logx)=e^(log)x^(2)))=x^(2)`
and general solution :
`y(x^(2))=intx log x*x^(2)dx+c`
`implies x^(2)y=intx^(3)logxdx+c`
`=logx*(x^(4))/(4)-int(x^(4))/(4)*(1)/(x)dx+c`
`=(x^(4))/(4)logx-(1)/(4)intx^(3)dx+c`
`=(x^(4))/(4)logx-(x^(4))/(16)+c`
`implies y=(1)/(16)x^(2)(4logx-1)+(c )/(x^(2))`