What is the solution for (dy)/(dx)=(-(3y)/(3x+2y)) ?

The solution for (dy)/(dx)=(-(3y)/(3x+2y)) is y=(-3x+sqrt(9x^2+c_{1)})/2 ,y=(-3x-sqrt(9x^2+c_{1)})/2

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(dy)/(dx)=(-(3y)/(3x+2y))

\frac{d y}{d x} = (- \frac{3 y}{3 x + 2 y})

y = \frac{- 3 x + 9 x ^{2} + c _{1}}{2}, y = \frac{- 3 x - 9 x ^{2} + c _{1}}{2}

Solution steps

\frac{d y}{d x} = (- \frac{3 y}{3 x + 2 y})

Solve exact ODE:

y = \frac{- 3 x + 9 x ^{2} + c _{1}}{2}, y = \frac{- 3 x - 9 x ^{2} + c _{1}}{2}

y = \frac{- 3 x + 9 x ^{2} + c _{1}}{2}, y = \frac{- 3 x - 9 x ^{2} + c _{1}}{2}

- 6 y^{^{''}} + 24 y = 0

\frac{\partial}{\partial y} (x y e^{x z})

x \to - \infty lim (x^{2} + 2 x)

\frac{d ^{2} x}{d x ^{2}}

\frac{d}{d x} (- \frac{15 x ^{4}}{2} + \frac{6 x ^{2}}{5} - \frac{x}{3} - 4)

What is the solution for (dy)/(dx)=(-(3y)/(3x+2y)) ?
The solution for (dy)/(dx)=(-(3y)/(3x+2y)) is y=(-3x+sqrt(9x^2+c_{1)})/2 ,y=(-3x-sqrt(9x^2+c_{1)})/2