Why Does My Differential Equation Solution Differ from the Textbook's?

jwxie
Messages
278
Reaction score
0

Homework Statement



\[\frac{\mathrm{dy} }{\mathrm{d} x} = \frac{x - e^{-x}}{y + e^{y}}<br /> \]


Homework Equations



The Attempt at a Solution



This is how I did it...
[1] multiple
\[y + e^{y} (dy) = x - e^{-x} (dx)\]

[2] integrate both sides and I get
\[\frac{1}{2}y^{2} + e^{y} = \frac{1}{2}x^{2} + e^{-x} +c\]

However, the solution gives
\[y^{2} - x^{2} +2(e^{y} - e^{-x}) = c\]
Notice the 2? I can't figure out what I did wrong.

I thank for any helps in advance!
Thanks.
 
Physics news on Phys.org
They just solved for c, then multiplied through by 2 to eliminate the 1/2's.
 
c is an arbitrary constant, your equation is the same as their's but, with 2c \rightarrow c. You are free to rename your arbitrary constants, as long as you do it consistently all throughout the equation.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top