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

Answer

` y=x^3/4 +c/x`

Explanation

We are given

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


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

here `P=1/x` and `Q=x^2`


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


General Solution is

`y*(I.F.)=int Q*(I.F.)dx +c`


`rArr y*x=int (x^2)*x dx +c`


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