My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Thanks Tree3Thanks
  • 2 Post By SenatorArmstrong
  • 1 Post By Joppy
Reply
 
LinkBack Thread Tools Display Modes
July 8th, 2017, 10:29 AM   #1
Member
 
Joined: Jan 2017
From: California

Posts: 65
Thanks: 5

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
dthiaw is offline  
 
July 8th, 2017, 10:33 AM   #2
Senior Member
 
SenatorArmstrong's Avatar
 
Joined: Nov 2015
From: Alabama

Posts: 113
Thanks: 15

Math Focus: Trigonometry, Calculus, 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 07:45 PM.
SenatorArmstrong is offline  
July 10th, 2017, 03:18 AM   #3
Senior Member
 
Joined: Feb 2016
From: Australia

Posts: 1,225
Thanks: 420

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 03:46 AM.
Joppy is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
constant, differential, equation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Linear Differential equation with constant coefficient Lalitha183 Differential Equations 2 June 4th, 2017 12:28 PM
Linear Ordinary Differential Equation with Constant Coefficients zylo Calculus 5 November 30th, 2016 07:56 PM
question about the constant when solving differential equations Jaket1 Differential Equations 3 March 16th, 2016 12:24 PM
Differential equation with constant delay (Urgent) rody Differential Equations 2 November 29th, 2013 05:59 PM
Linear differential equations with constant coefficients jokes_finder Differential Equations 3 November 20th, 2010 10:52 AM





Copyright © 2017 My Math Forum. All rights reserved.