What is the solution for (dy)/(dx)=8x^3e^{-2y},y(1)=0 ?

The solution for (dy)/(dx)=8x^3e^{-2y},y(1)=0 is y=(ln(4x^4-3))/2

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(dy)/(dx)=8x^3e^{-2y},y(1)=0

\frac{d y}{d x} = 8 x^{3} e^{- 2 y}, y (1) = 0

y = \frac{ln ( 4 x ^{4} - 3 )}{2}

Solution steps

\frac{d y}{d x} = 8 x^{3} e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( 4 x ^{4} - 3 )}{2}

y = \frac{ln ( 4 x ^{4} - 3 )}{2}

\frac{d}{d x} (\frac{x ^{2} + 14}{x ^{8}})

y^{^{''}} + 4 y^{^{'}} + 6.25 y = 3.125 (x + 1)^{2}

y^{^{'}} = 2 x y^{- 2}

\frac{d}{d x} (ln^{2} (1 - 2 x))

f (x) = \frac{x}{ln ( x )}

What is the solution for (dy)/(dx)=8x^3e^{-2y},y(1)=0 ?
The solution for (dy)/(dx)=8x^3e^{-2y},y(1)=0 is y=(ln(4x^4-3))/2