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}

\frac{\partial}{\partial x} (x^{2} + z^{2})

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{4 x - 3})

g (x) = 3 e^{x} x

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

\frac{\partial}{\partial x} (x yz + 9 x + 8 y - 4 z)

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