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Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^...

Solve `(x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)`

Text Solution

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`(x+y(dy)/(dx))/(y-x(dy)/(dx))=x^(2)+2y^(2)+y^(4)/x^(2)`
or `(xdx+ydy)/((x^(2)+y^(2))^(2)) = (ydx-xdy)/(y^(2))y^(2)/x^(2)`
or `intd(x^(2)+y^(2))/(x^(2)+y^(2))^(2)=-2int1/(x^(2)//y^(2))d(x/y)`
or `-1/(x^(2)+y^(2))=-2/(x//y)+c`
or `(2y)/(x) -1/(x^(2)+y^(2))=c`
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