What is the solution for (dy)/(dx)=y(2x^2+1) ?

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

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(dy)/(dx)=y(2x^2+1)

\frac{d y}{d x} = y (2 x^{2} + 1)

y = e^{\frac{2 x ^{3}}{3} + x + c_{1}}

Solution steps

\frac{d y}{d x} = y (2 x^{2} + 1)

Solve separable ODE:

y = e^{\frac{2 x ^{3}}{3} + x + c_{1}}

y = e^{\frac{2 x ^{3}}{3} + x + c_{1}}

\frac{d y}{d x} = (\frac{x ^{2} - 1}{y ^{2}})

\frac{d y}{d x} = y (2 x^{2} + 4)

(3 x^{2} y + 2 y) d x + (x^{3} + 2 x) d y = 0

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

\frac{d y}{d x} = \frac{( 3 e ^{x} )}{( 3 y + 1 )}

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