Differential Equations Ordinary and Partial Differential Equations Math Forum

September 5th, 2018, 10:01 PM   #21
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Quote:
 Originally Posted by babaliaris So back to the problem : Finally: $\displaystyle f(x) = \frac{1}{-1 - ke^{-x}}$
Καλημέρα,

What we get from condition $\displaystyle f(x)-f'(x)>0$?

Όλα o καλός,

Integrator

Last edited by Integrator; September 5th, 2018 at 10:32 PM. September 6th, 2018, 10:05 PM   #22
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Quote:
 Originally Posted by babaliaris Finally: $\displaystyle f(x) = \frac{1}{-1 - ke^{-x}}$
Hello,

From the calculations it follows that $\displaystyle f:\mathbb C$ $\displaystyle \rightarrow \mathbb C$ where $\displaystyle f(x) = \frac{1}{-1 - ke^{-x}}$ , $\displaystyle f(x)-f'(x)=a^2$ with $\displaystyle a\cdot k\neq 0$ , $\displaystyle a\in \mathbb R$ , $\displaystyle a\cdot k\neq 0$ and thus $\displaystyle x=2i\pi n+\log \bigg (-\frac{ak}{a\mp i}\bigg )$ where $\displaystyle i^2=-1$.

All the best,

Integrator September 7th, 2018, 03:56 AM   #23
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Quote:
 Originally Posted by Integrator Is it correct what WolframAlpha says?
Strictly speaking, no. September 7th, 2018, 06:51 AM #24 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra I don't know about "strictly". The only way it could be partially true is if $x$ is complex. If $x \in \mathbb R$, the given solutions are false. But in either case, the solution $f(x)=0$ has been omitted. It corresponds to the limiting cases \begin{align}f(x) &=\lim_{c \to \pm\infty} \frac{e^x}{c+e^x} = 0 \\ f(x) &=\lim_{c \to -\infty} -\frac{e^{c+x}}{e^{c+x}-1} = 0 \end{align} Graph of WA Solutions Tags differential, equation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jiasyuen Calculus 1 June 26th, 2016 02:04 PM Sonprelis Calculus 6 August 6th, 2014 10:07 AM interestedinmaths Differential Equations 2 January 22nd, 2014 02:15 AM PhizKid Differential Equations 0 February 24th, 2013 10:30 AM golomorf Differential Equations 4 August 6th, 2012 09:40 AM

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