What is the solution for (dy)/(dx)=y(4x^2+6) ?

The solution for (dy)/(dx)=y(4x^2+6) is y=e^{(4x^3)/3+6x+c_{1}}

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(dy)/(dx)=y(4x^2+6)

\frac{d y}{d x} = y (4 x^{2} + 6)

y = e^{\frac{4 x ^{3}}{3} + 6 x + c_{1}}

Solution steps

\frac{d y}{d x} = y (4 x^{2} + 6)

Solve separable ODE:

y = e^{\frac{4 x ^{3}}{3} + 6 x + c_{1}}

y = e^{\frac{4 x ^{3}}{3} + 6 x + c_{1}}

y^{^{''}} - 6 y^{^{'}} + 3 y = 0, y (0) = 0, y^{^{'}} (0) = 5

y^{^{'}} = \frac{( 3 x ^{2} - e ^{x} )}{( 2 y - 5 )}

h \to 0 lim (\frac{( 3 + h ) ^{2} - 9}{h})

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

f (x) = \frac{3}{t}

What is the solution for (dy)/(dx)=y(4x^2+6) ?
The solution for (dy)/(dx)=y(4x^2+6) is y=e^{(4x^3)/3+6x+c_{1}}