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}}

(1 - y^{2}) d x + x d y = 0

\frac{d y}{d x} - 2 x y = 2 x, y (0) = 3

\frac{d y}{d x} = 3 \frac{y ^{5}}{x ^{4}}

y^{^{'}} + \frac{4}{20 + t} y = 0

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