# Differential Equation - Hermite's Equation

## Homework Statement

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

## 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.

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rock.freak667
Homework Helper

## Homework Statement

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

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

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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.

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

Pengwuino
Gold Member
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?

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

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.