What is the solution for (dy)/(dx)=(3x^2)/(e^{2y)},y(0)= 1/2 ?

The solution for (dy)/(dx)=(3x^2)/(e^{2y)},y(0)= 1/2 is y=(ln(2x^3+e))/2

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(dy)/(dx)=(3x^2)/(e^{2y)},y(0)= 1/2

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{2 y}}, y (0) = \frac{1}{2}

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

Solution steps

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

Solve separable ODE:

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

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

2 x (x^{2} - 4 x + 5)^{8}, at x = 2

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 t^{3}

(\frac{2}{x ^{3}})^{^{'}}

y = \frac{1}{3} x^{3}

\int e^{- 0.2 x} d x

What is the solution for (dy)/(dx)=(3x^2)/(e^{2y)},y(0)= 1/2 ?
The solution for (dy)/(dx)=(3x^2)/(e^{2y)},y(0)= 1/2 is y=(ln(2x^3+e))/2