What is the solution for (dy)/(dx)=y(4x^2+5) ?

The solution for (dy)/(dx)=y(4x^2+5) is y=e^{(4x^3)/3+5x+c_{1}}

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(dy)/(dx)=y(4x^2+5)

\frac{d y}{d x} = y (4 x^{2} + 5)

y = e^{\frac{4 x ^{3}}{3} + 5 x + c_{1}}

Solution steps

\frac{d y}{d x} = y (4 x^{2} + 5)

Solve separable ODE:

y = e^{\frac{4 x ^{3}}{3} + 5 x + c_{1}}

y = e^{\frac{4 x ^{3}}{3} + 5 x + c_{1}}

x^{^{'}} = (x)^{4 (1) + 2} (ln (t) + (0 + 2) t e^{t})

\frac{x}{y} d x + \frac{y}{x} d y = 0

x^{^{'}} = e^{x} \frac{1}{t}

(3 x - 5) d x + (y + b) d y = 0

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

What is the solution for (dy)/(dx)=y(4x^2+5) ?
The solution for (dy)/(dx)=y(4x^2+5) is y=e^{(4x^3)/3+5x+c_{1}}