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

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

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(dy)/(dx)= 1/4 e^{-2y},y(0)=0

\frac{d y}{d x} = \frac{1}{4} e^{- 2 y}, y (0) = 0

y = \frac{ln ( \frac{x}{2} + 1 )}{2}

Solution steps

\frac{d y}{d x} = \frac{1}{4} e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( \frac{x}{2} + 1 )}{2}

y = \frac{ln ( \frac{x}{2} + 1 )}{2}

\frac{d y}{d x} = \frac{( 2 y ln ( y ) )}{( x )}, y (1) = 4

y \frac{d y}{d x} - x y^{2} + x = 0

y^{^{'}} - 6 x y = 0, y (1) = 1

- x y + (1 - x^{2}) (\frac{d y}{d x}) = 7 x y^{2}

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

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