What is the solution for (dy)/(dx)=-y(x^2+6) ?

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

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(dy)/(dx)=-y(x^2+6)

\frac{d y}{d x} = - y (x^{2} + 6)

y = e^{- \frac{x ^{3}}{3} - 6 x + c_{1}}

Solution steps

\frac{d y}{d x} = - y (x^{2} + 6)

Solve separable ODE:

y = e^{- \frac{x ^{3}}{3} - 6 x + c_{1}}

y = e^{- \frac{x ^{3}}{3} - 6 x + c_{1}}

\frac{1}{y ^{^{'}}} = \frac{2 y}{x}

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

y^{^{'}} = - x y, y (0) = 1

x (x - 1) \frac{d y}{d x} = y

\frac{d y}{d x} = (\frac{y}{20000}) x

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