# Thread: Differentiable Eq. finding function f

1. ## Differentiable Eq. finding function f

Find the function $\displaystyle f$ such that $\displaystyle f'(x) = f(x)(1 - f(x))$ and $\displaystyle f(0) = \frac{1}{2}$.

We are currently covering separable differentiable eq. and this problem is throwing me for a loop.

Any hints for a starting point?

I know
$\displaystyle f(x) = \int(f(x)(1 - f(x)))$ thus $\displaystyle \frac{1}{2} = \int(f(0)(1 - f(0)))$. Then I am lost. How can you find f if you can't separate the x's and y's?

2. Originally Posted by diablo2121
Find the function $\displaystyle f$ such that $\displaystyle f'(x) = f(x)(1 - f(x))$ and $\displaystyle f(0) = \frac{1}{2}$.

We are currently covering separable differentiable eq. and this problem is throwing me for a loop.

Any hints for a starting point?

I know
$\displaystyle f(x) = \int(f(x)(1 - f(x)))$ thus $\displaystyle \frac{1}{2} = \int(f(0)(1 - f(0)))$. Then I am lost. How can you find f if you can't separate the x's and y's?
You might find the problem easier by using the following notation:

Solve $\displaystyle \frac{dy}{dx} = y(1 - y)$ where $\displaystyle y = \frac{1}{2}$ when x = 0.