`x(dy)/(dx)=y`

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x(dy)/(dx)=x+y

y-x(dy)/(dx)=x+y(dy)/(dx)

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y^2+x^2(dy)/(dx)=x y(dy)/(dx)

(x-y)(dy)/(dx)=x+3y

The solution of the differential equation x dx + y dy+ (x dy - y dx)/(x^(2)+y^(2))=0 is

Solve: x dx+y dy=x dy-y dx