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}

\int \frac{3}{x ^{2} - 8 x + 6} d x

k = 0 \sum \infty x^{k + 1}

y = (3 x + 8) x^{2}

x \to 2 - lim (x^{2} + 1)

\frac{d y}{d x}, x y = 9

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