My Math Forum Constant C in differential equation

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 July 8th, 2017, 11:29 AM #1 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 Constant C in differential equation Hi guys, $$\int {}\frac{1}{ky}dy =\int dx \rightarrow \frac{1}{k}\ln \left | y \right |=x+C$$ Why is C only on the right side and not on the left side? Thanks in advance
 July 8th, 2017, 11:33 AM #2 Senior Member     Joined: Nov 2015 From: United States of America Posts: 181 Thanks: 21 Math Focus: Calculus and Physics You can put a 'c' on both sides if you want. C is an arbitrary constant. You can combine all constants to form one final constant. $$\int {}\frac{1}{ky}dy =\int dx \rightarrow \frac{1}{k}\ln \left | y \right | + C1 =x+C2$$ $$\rightarrow \frac{1}{k}\ln \left | y \right | =x+C2 - C1$$ $$\rightarrow C2 - C1 = C$$ $$\rightarrow \frac{1}{k}\ln \left | y \right | =x+C$$ Thanks from Country Boy and dthiaw Last edited by skipjack; July 8th, 2017 at 08:45 PM.
 July 10th, 2017, 04:18 AM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,734 Thanks: 605 Math Focus: Yet to find out. Might also be worth keeping in mind that the general solution of an $nth$ order differential equation will contain $n$ arbitrary constants. Thanks from dthiaw Last edited by skipjack; July 10th, 2017 at 04:46 AM.

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