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}

(9 + x) \frac{d y}{d x} = 6 + x

\frac{d}{d x} (\frac{x y}{2})

\frac{\partial}{\partial y} (- 20 x y^{2} + 6 x)

x y^{^{'}} = y^{2}, y (1) = 1

t \cdot y^{^{'}} - 3 \cdot y = t^{4}

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