Solve `(dy)/(dx)=(2x-y+1)/(x+2y-3)`

Answer

`xy+y^(2)-3y=x^(2)+x+c`

Explanation

Here, `(dy)/(dx)=(2x-y+1)/(x+2y-3)`
Cross multiplying, we get
`xdy+(2y-3)dy=(2x+1)dx-ydx`
or `(xdy+ydx)+(2y-3)dy=(2x+1)dx`
or `d(xy)+(2y-3)dy=(2x+1)dx`
Integrating, we get
`xy+y^(2)-3y=x^(2)+x+c`