What is the solution for (dy)/(dx)+3ex^2y=6x^2 ?

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

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(dy)/(dx)+3ex^2y=6x^2

\frac{d y}{d x} + 3 e x^{2} y = 6 x^{2}

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

Solution steps

\frac{d y}{d x} + 3 e x^{2} y = 6 x^{2}

Solve separable ODE:

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

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

\frac{d y}{d x} = 2 y^{2}, x = 2

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

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

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