My Math Forum  

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

Differential Equations Ordinary and Partial Differential Equations Math Forum


Thanks Tree6Thanks
  • 2 Post By romsek
  • 1 Post By Joppy
  • 2 Post By skipjack
  • 1 Post By topsquark
Reply
 
LinkBack Thread Tools Display Modes
June 9th, 2019, 03:50 AM   #1
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 534
Thanks: 81

Equation : $\displaystyle y’’=y$.
Add both sides +y’ then substitution as $\displaystyle y’+y=t$.
$\displaystyle t’=t$.
Is this way correct?

Last edited by skipjack; June 9th, 2019 at 10:18 AM.
idontknow is offline  
 
June 9th, 2019, 05:25 AM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,452
Thanks: 1337

The usual way is to form the characteristic equation.

$y''-y=0$

$s^2 - 1= 0$

$s = \pm 1$

$y = c_1 e^t + c_2 e^{-t}$
Thanks from topsquark and idontknow
romsek is online now  
June 9th, 2019, 08:08 AM   #3
Senior Member
 
Joined: Feb 2016
From: Australia

Posts: 1,821
Thanks: 643

Math Focus: Yet to find out.
Also the chant "what when differentiated twice equals itself!"
Thanks from idontknow
Joppy is offline  
June 9th, 2019, 10:02 AM   #4
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,452
Thanks: 1337

Quote:
Originally Posted by Joppy View Post
Also the chant "what when differentiated twice equals itself!"
I don't remember hearing that one down the pub.
romsek is online now  
June 9th, 2019, 10:24 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,746
Thanks: 2133

Quote:
Originally Posted by idontknow View Post
Is this way correct?
Yes. Having found $t$, you could then solve $y' + y = t$ by using an integrating factor.

The same integrating factor works for the original equation.

Integrating $e^xy'' - e^xy = 0$ gives $e^xy' - e^xy = \text{A}$, etc.
Thanks from topsquark and idontknow
skipjack is offline  
June 9th, 2019, 02:40 PM   #6
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 2,194
Thanks: 897

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by romsek View Post
I don't remember hearing that one down the pub.
Apparently you go to the wrong bars.

-Dan
Thanks from Joppy
topsquark is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
check, method



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Why first method answer didn't match second method? Ganesh Ujwal Algebra 8 October 5th, 2018 05:36 AM
good/bad of simplex method and big M method carlluis Linear Algebra 1 April 5th, 2018 10:49 AM
Vector projection ans check and derivation check taylor_1989_2012 Pre-Calculus 1 October 27th, 2016 05:33 PM
check method taylor_1989_2012 Trigonometry 2 March 12th, 2016 09:00 AM
Can someone check this? eddybob123 Number Theory 9 March 20th, 2013 03:25 PM





Copyright © 2019 My Math Forum. All rights reserved.