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

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

Text Solution

Verified by Experts

The correct Answer is:
`xy+y^(2)-3y=x^(2)+x+c`
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`
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