Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

General solution for this differential equation??

Find a general solution to

y′′′ − y′′ + 2y = 0

I have never dealt with 3rd order D.E before. I hope you have!

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: General solution for this differential equation??

(1/12)y^4 = (1/2)y^2 - y + (1/2)C[1]y^2 + C[2]y - C[3]

Is that the answer?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: General solution for this differential equation??

@Agnishom;

These are solved using the characteristic or auxiliary polynomial or try this:

DSolve[{y'''[x] - y''[x] + 2 y[x] == 0}, y[x], x]

Hi mrpace;

Here is a so-so explanation:

http://www.math.upenn.edu/~moose/240S20 … es8-05.pdf

The auxiliary equation is

and the roots are:

r1 = -1

r2 = 1 + i

r3 = 1 - i

can you finish now?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.