Find the equation of the curve passing through the point `(1,1)` whose differential equation is : `xdy=(2x^2+1)dxdot`

Answer

`y=x^2+ log|x|`

Explanation

We are given the differential equation


`xdy=(2x^2+1)dx`


Simplifying,


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


`rArr dy=(2x+1/x)dx`


Integrating both sides we get,


`int dy=int (2x+1/x)dx`


`rArr int dy=int 2xdx+ int 1/xdx`


...