What is the solution for (dy)/(dx)=(x+3y)/(y-3x) ?

The solution for (dy)/(dx)=(x+3y)/(y-3x) is y=(6x+sqrt(40x^2+c_{1)})/2 ,y=(6x-sqrt(40x^2+c_{1)})/2

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(dy)/(dx)=(x+3y)/(y-3x)

\frac{d y}{d x} = \frac{x + 3 y}{y - 3 x}

y = \frac{6 x + 40 x ^{2} + c _{1}}{2}, y = \frac{6 x - 40 x ^{2} + c _{1}}{2}

Solution steps

\frac{d y}{d x} = \frac{x + 3 y}{y - 3 x}

Solve exact ODE:

y = \frac{6 x + 40 x ^{2} + c _{1}}{2}, y = \frac{6 x - 40 x ^{2} + c _{1}}{2}

y = \frac{6 x + 40 x ^{2} + c _{1}}{2}, y = \frac{6 x - 40 x ^{2} + c _{1}}{2}

\int n^{x} d x

y = - 25 + 5 x + 10 e^{- \frac{x}{5} + 1}

y^{^{'}} - 7.5 y = - 12 y^{2}

\frac{\partial}{\partial y} (7 e^{yz} cos (x yz))

\frac{d}{d x} (x + x + 7)

What is the solution for (dy)/(dx)=(x+3y)/(y-3x) ?
The solution for (dy)/(dx)=(x+3y)/(y-3x) is y=(6x+sqrt(40x^2+c_{1)})/2 ,y=(6x-sqrt(40x^2+c_{1)})/2