What is the solution for (dy)/(dx)=(3y)/(x+6) ?

The solution for (dy)/(dx)=(3y)/(x+6) is y=e^{c_{1}}x^3+18e^{c_{1}}x^2+108e^{c_{1}}x+216e^{c_{1}}

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(dy)/(dx)=(3y)/(x+6)

\frac{d y}{d x} = \frac{3 y}{x + 6}

y = e^{c_{1}} x^{3} + 18 e^{c_{1}} x^{2} + 108 e^{c_{1}} x + 216 e^{c_{1}}

Solution steps

\frac{d y}{d x} = \frac{3 y}{x + 6}

Solve separable ODE:

y = e^{c_{1}} x^{3} + 18 e^{c_{1}} x^{2} + 108 e^{c_{1}} x + 216 e^{c_{1}}

y = e^{c_{1}} x^{3} + 18 e^{c_{1}} x^{2} + 108 e^{c_{1}} x + 216 e^{c_{1}}

y^{^{'}} [t] = 0.3 y [t]

32 = v^{2} + xv \frac{d v}{d x}

3 y \frac{d y}{d x} = 2 x^{2} - 3

\frac{d y}{d x} = y^{2} + 2 y - 15

y^{^{'}} = x y^{3} (1 + x^{2})^{(\frac{- 1}{2})}

What is the solution for (dy)/(dx)=(3y)/(x+6) ?
The solution for (dy)/(dx)=(3y)/(x+6) is y=e^{c_{1}}x^3+18e^{c_{1}}x^2+108e^{c_{1}}x+216e^{c_{1}}