What is the solution for (x+y)dx+(x-y)dy=0 ?

The solution for (x+y)dx+(x-y)dy=0 is y=-(-2x+sqrt(8x^2-c_{1)})/2 ,y=-(-2x-sqrt(8x^2-c_{1)})/2

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(x+y)dx+(x-y)dy=0

(x + y) d x + (x - y) d y = 0

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 + (x - y) d y = 0

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}

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What is the solution for (x+y)dx+(x-y)dy=0 ?
The solution for (x+y)dx+(x-y)dy=0 is y=-(-2x+sqrt(8x^2-c_{1)})/2 ,y=-(-2x-sqrt(8x^2-c_{1)})/2