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

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

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

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

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

Solution steps

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

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}

y^{'} = y^{2} - 4

(x^{2} + 4) (\frac{d y}{d x}) = x y

\int x^{3} x^{2} + 40 d x

\frac{4}{x ^{2}}

\int \frac{( x - 95 )}{x ^{2} ( x + 5 )} d x

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