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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

P^{^{'}} = (P) (t) (1 - \frac{P}{10})

(1 + x^{2}) \cdot y^{^{'}} + \frac{y}{arctan ( x )} = 0

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

y^{^{'}} = \frac{y + 9}{x + 8}

\frac{d y}{d t} + 20 y = 2, 4 = \frac{6}{5} - \frac{6}{5} e^{- 20 t}

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