First oder differential equation.

Zubz
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Homework Statement


Hi, i have a question.
1. find the function f(x).
f'(x) = f(x)(1- f(x)) f(0) = 1/8 ---> intial value problem.

Homework Equations





The Attempt at a Solution


y' = y(1 - y)
y' = y - y2
and now i don't know how/ what to do.
 
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\frac{dy}{dt}= y(1- y)
so
\frac{dy}{y(1- y)}= dt

Now integrate on both sides.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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