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

The solution for (dy)/(dx)=(y^2)/(e^x),y(0)=-2 is y=-(2e^x)/(-2+3e^x)

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(dy)/(dx)=(y^2)/(e^x),y(0)=-2

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

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

Solution steps

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

Solve separable ODE:

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

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

y = x^{2}, (0, - 4)

x \to \infty lim (\frac{x}{ln ( x )})

\frac{d}{d x} (\frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}})

\int e^{2 x} (1 - 2 e^{2 x})^{2} d x

\int (e^{4 x} - \frac{3}{e ^{\frac{x}{2}}}) d x

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