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

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

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

\frac{d y}{d x} (x + y) = x - y

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

Solution steps

\frac{d y}{d x} (x + y) = x - 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}

\frac{d}{d t} (- e^{2 t})

\int \frac{x}{2 x - x ^{2}} d x

x \to 0 lim (\frac{cos ( 2 x ) - cos ( 5 x )}{x ^{2}})

\int_{- 4}^{4} \frac{1}{2} (16 - x^{2}) d x

\int_{6}^{8} \frac{54}{( x - 6 ) ^{3}} d x

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