• Support PF! Buy your school textbooks, materials and every day products Here!

Differential Equation - Hermite's Equation

  • Thread starter cse63146
  • Start date
  • #1
452
0

Homework Statement



Find the general solution of y' + 2ty = 0

Homework Equations





The Attempt at a Solution



so I know y = [tex]\Sigma^{\infty}_{n=0} a_n t^n[/tex] and y' =[tex]\Sigma^{\infty}_{n=1} n a_n t^{n-1}[/tex]

not sure what to do next.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31

Homework Statement



Find the general solution of y' + 2ty = 0

Homework Equations





The Attempt at a Solution



so I know y = [tex]\Sigma^{\infty}_{n=0} a_n t^n[/tex] and y' =[tex]\Sigma^{\infty}_{n=1} n a_n t^{n-1}[/tex]

not sure what to do next.
http://www.sosmath.com/diffeq/series/series06/series06.html" [Broken]
 
Last edited by a moderator:
  • #3
152
0
Is that first line a typo? Should it be y'' (two primes, second derivative)? I'm guessing it is because the link shows a second order DE.

If it is a single prime, then you could do a simple integration to get the answer, unless you have been told to use a series solution.
 
  • #4
452
0
It's y' + 2ty = 0. Makes the problem a bit easier.
 
  • #5
Pengwuino
Gold Member
4,989
15
Yah wait a minute, what does that equation have to do with Hermite's equation? Are you SURE it isn't a second order differential equation?
 
  • #6
3
0
Find the general solution of y' + 2ty = 0
Do you have a prescribed method (like series?)
If not, it is very simple
Devide the Eq by y and you get
y´/y = -2t
Integrate
ln(y) = -t2
y=exp(-t2) + C
that is the general solution
 
  • #7
452
0
It might not be (even though its in the same section). But I wanted to try and solve that before I move on to the second order version.
 

Related Threads for: Differential Equation - Hermite's Equation

Replies
4
Views
2K
Replies
2
Views
1K
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
796
  • Last Post
Replies
0
Views
2K
Top