What is the solution for (x+y)dx=(y-x)dy ?

The solution for (x+y)dx=(y-x)dy is y=-(-2x+sqrt(8x^2-c_{1)})/2 ,y=-(-2x-sqrt(8x^2-c_{1)})/2

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

(x + y) d x = (y - x) d y

y = - \frac{- 2 x + 8 x ^{2} - c _{1}}{2}, y = - \frac{- 2 x - 8 x ^{2} - c _{1}}{2}

Solution steps

(x + y) d x = (y - x) d y

Solve exact ODE:

y = - \frac{- 2 x + 8 x ^{2} - c _{1}}{2}, y = - \frac{- 2 x - 8 x ^{2} - c _{1}}{2}

y = - \frac{- 2 x + 8 x ^{2} - c _{1}}{2}, y = - \frac{- 2 x - 8 x ^{2} - c _{1}}{2}

What is the solution for (x+y)dx=(y-x)dy ?
The solution for (x+y)dx=(y-x)dy is y=-(-2x+sqrt(8x^2-c_{1)})/2 ,y=-(-2x-sqrt(8x^2-c_{1)})/2