Solve the differential equation: `x(dy)/(dx)+2y=x^2,\ x!=0`

Answer

`y=x^2/4+cx^(-2)`

Explanation

We are given

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


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


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


`therefore` I.F.`=e^(int 2/xdx)=e^(2logx)=e^(log x^2)=x^2`


General solution is:

`yx^2=int x*x^2dx+c`


`rArr yx^2=x^4/4+c`


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