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y(x^(2)y+e^(x))dx-e^(x)dy=0...

`y(x^(2)y+e^(x))dx-e^(x)dy=0`

Text Solution

Verified by Experts

The correct Answer is:
`x^(3)y+3e^(x)=cy`
`y(x^(2)y+e^(x))dx-e^(x)dy=0`
or `ye^(x)dx-e^(x)dy+x^(2)y^(2)dx=0`
or `(ye^(x)dx-e^(x)dy)/(y^(2))+x^(2)dx=0`
`d(e^(x)y)+x^(2)dx=0`
Integrating, we get
`e^(x)/y+x^(3)/3=k`
or `x^(3)y+3e^(x)=3ky`
or `x^(3)y+3e^(x)=Cy`
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