What is the solution for (dy)/(dx)=y(1-y),y(0)=8 ?

The solution for (dy)/(dx)=y(1-y),y(0)=8 is y=(8e^x)/(-7+8e^x)

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(dy)/(dx)=y(1-y),y(0)=8

\frac{d y}{d x} = y (1 - y), y (0) = 8

y = \frac{8 e ^{x}}{- 7 + 8 e ^{x}}

Solution steps

\frac{d y}{d x} = y (1 - y)

Solve Bernoulli ODE:

y = \frac{8 e ^{x}}{- 7 + 8 e ^{x}}

y = \frac{8 e ^{x}}{- 7 + 8 e ^{x}}

x \to 4 - lim (3 x - 5)

4 x^{3} - 56 x^{2} + 196 x

\int \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} d x

\int 2 x^{3} e^{- 2 x} d x

x \to \frac{π}{4} lim (\frac{cos ( 2 x )}{2 cos ( x ) - 1})

What is the solution for (dy)/(dx)=y(1-y),y(0)=8 ?
The solution for (dy)/(dx)=y(1-y),y(0)=8 is y=(8e^x)/(-7+8e^x)