My Math Forum  

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

Differential Equations Ordinary and Partial Differential Equations Math Forum


Thanks Tree2Thanks
  • 2 Post By topsquark
Reply
 
LinkBack Thread Tools Display Modes
May 21st, 2019, 05:10 PM   #1
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 634
Thanks: 91

Differential equation

$\displaystyle \frac{d^4 z}{dt^4 }=z+C \; $ , C-constant .

To get at least one solution , apply derivatives to equallity : $\displaystyle z^{(5)}=z'$ , How to get the general solution ?

Last edited by idontknow; May 21st, 2019 at 05:17 PM.
idontknow is offline  
 
May 21st, 2019, 06:38 PM   #2
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 2,266
Thanks: 934

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by idontknow View Post
$\displaystyle \frac{d^4 z}{dt^4 }=z+C \; $ , C-constant .

To get at least one solution, apply derivatives to equality: $\displaystyle z^{(5)}=z'$. How to get the general solution?
To get the homogenous equation:
$\displaystyle \dfrac{d^4 z}{dt^4} - z = 0$

The characteristic equation is $\displaystyle m^4 - 1 = 0$, which has solutions 1, -1, i, -i. Thus the homogeneous solution is of the form:
$\displaystyle z_h(t) = Ae^t + Be^{-t} + D~\sin(t) + E~\cos(t)$.

Or, if you prefer
$\displaystyle z_h(t) = Ae^t + Be^{-1} + De^{it} + Ee^{-it}$
(The D's and E's are different from each other in the two equations.)

Can you finish?

-Dan
Thanks from idontknow and Greens

Last edited by skipjack; May 22nd, 2019 at 12:07 AM.
topsquark is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
differential, equation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Differential equation Tamer Ghareeb Differential Equations 5 December 7th, 2015 12:30 AM
Gompertz equation - differential equation Sonprelis Calculus 6 August 6th, 2014 10:07 AM
Show that an equation satisfies a differential equation PhizKid Differential Equations 0 February 24th, 2013 10:30 AM
Differential equation Vasily Differential Equations 4 June 4th, 2012 02:17 AM
differential equation main Differential Equations 1 July 3rd, 2009 09:52 AM





Copyright © 2019 My Math Forum. All rights reserved.