What is the solution for (dy)/(dx)=(x-y)/(x+2y) ?

The solution for (dy)/(dx)=(x-y)/(x+2y) is y=(-x+sqrt(3x^2+c_{1)})/2 ,y=-(x+sqrt(3x^2+c_{1)})/2

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(dy)/(dx)=(x-y)/(x+2y)

\frac{d y}{d x} = \frac{x - y}{x + 2 y}

y = \frac{- x + 3 x ^{2} + c _{1}}{2}, y = - \frac{x + 3 x ^{2} + c _{1}}{2}

Solution steps

\frac{d y}{d x} = \frac{x - y}{x + 2 y}

Solve exact ODE:

y = \frac{- x + 3 x ^{2} + c _{1}}{2}, y = - \frac{x + 3 x ^{2} + c _{1}}{2}

y = \frac{- x + 3 x ^{2} + c _{1}}{2}, y = - \frac{x + 3 x ^{2} + c _{1}}{2}

What is the solution for (dy)/(dx)=(x-y)/(x+2y) ?
The solution for (dy)/(dx)=(x-y)/(x+2y) is y=(-x+sqrt(3x^2+c_{1)})/2 ,y=-(x+sqrt(3x^2+c_{1)})/2