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Solve the differential equation y e^(x/y...

Solve the differential equation `y e^(x/y)dx=(x e^(x/y)+y^2siny)dy(y!=0)`

Text Solution

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We have `ye^(x/y)dx-xe^(x/y)dy=y^(2)dy`
`therefore e^(x/y)(ydx-xdy)/(y^(2))=dy`
`rArr inte^(x/y)d(x/y)=intdy`
`rArr e^(x/y)=y+c`.
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