What is the solution for y^'=sqrt((1-y^2)/(e^x)) ?

The solution for y^'=sqrt((1-y^2)/(e^x)) is y=sin(x/(e^{x/2)}-e^{-x/2}(x+2)+c_{1})

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y^'=sqrt((1-y^2)/(e^x))

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

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

Solution steps

y^{'} (x) = \frac{1 - y ^{2}}{e ^{x}}

Solve separable ODE:

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

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

n = 0 \sum \infty p^{n}

x \to 3 lim (6 x)

\int \frac{q}{π ( - 0.125 x + 0.03125 ) ^{2}} d x

\int \frac{1}{2 - 2 x} d x

\frac{d}{d t} (\frac{t}{10} sin (5 t))

What is the solution for y^'=sqrt((1-y^2)/(e^x)) ?
The solution for y^'=sqrt((1-y^2)/(e^x)) is y=sin(x/(e^{x/2)}-e^{-x/2}(x+2)+c_{1})