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

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

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

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

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

Solution steps

(y + x) \frac{d y}{d x} = 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{\partial}{\partial x} (ln (x + y + z))

f (x) = \frac{1}{2} e^{2 x}

\int x^{2} - 3 x + 2 d x

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\frac{d}{d x} (1 + 2 x^{2})

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