# Differential Equation - Hermite's Equation

1. May 24, 2009

### cse63146

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

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

not sure what to do next.

2. May 24, 2009

### rock.freak667

http://www.sosmath.com/diffeq/series/series06/series06.html" [Broken]

Last edited by a moderator: May 4, 2017
3. May 24, 2009

### Chrisas

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. May 24, 2009

### cse63146

It's y' + 2ty = 0. Makes the problem a bit easier.

5. May 24, 2009

### Pengwuino

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. May 25, 2009

### zebra

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. May 25, 2009

### cse63146

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.

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