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}}

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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)