How to solve this ordinary differential equation?
$$ \frac{1}{m}(\log f(x))'=f(x)-1,\,\,m>0. $$
Is this equation solvable? Is so, can anyone give me a hint?
Thanks a lot.
$\begingroup$ $\endgroup$
Add a comment |
1 Answer
$\begingroup$ $\endgroup$
The equation is soluble. Write $y=f(x)$ and
$$\frac{d}{dx} \log{y} = \frac{y'}{y}$$
Then you can show that the equation may be rewritten as
$$\frac{y'}{y (y-1)} = m$$
Integrate both sides with respect to $x$ and solve for $y$.
