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Solve the differential equation : xdy+ ...

Solve the differential equation : ` xdy+ ydx + ( xdy- ydx ) /( x^2 + y^2)=0`

Text Solution

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We have,
`xdy+ydx=(xdy-ydx)/(x^(2)+y^(2))`
`therefore d(xy) = ((xdy-ydx)/(x^(2)))/(1(y/x)^(2))`
`rArr intd(xy) = int (d(y/x))/(1+(y/x)^(2))`
`rArr xy-tan^(-)y/x+c`
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