Differential Equation - Hermite's Equation

[cse63146]

Homework Statement

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

Homework Equations

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.

 

[rock.freak667]

Homework Statement

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

Homework Equations

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"

 

[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.

 

[cse63146]

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

 

[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?

 

[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

 

[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.