Is there any book talking about system of 2nd order ODE?

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Discussion Overview

The discussion revolves around finding resources, specifically books, that address systems of second-order ordinary differential equations (ODEs). Participants share their experiences and suggestions related to the topic, including methods for transforming second-order equations into systems.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant expresses difficulty in dealing with a specific system of second-order ODEs and requests book recommendations.
  • Another participant suggests that a second-order differential equation can be transformed into a system by introducing a new variable, v, defined as y'.
  • A follow-up question arises regarding the definition of y in this context.
  • A participant shares a link to a resource that may assist with solving nth-order linear differential equations.
  • One participant recommends "Nonlinear Dynamics and Chaos" by Strogatz as a valuable book on systems of ODEs, noting its relevance to the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best resource, and multiple suggestions and methods for addressing the problem are presented, indicating a variety of perspectives on the topic.

Contextual Notes

The discussion includes assumptions about the transformation of second-order equations and the definitions of variables, which remain unresolved.

ck00
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I got trouble in dealing with this kind of system. For example,
Ay``+By`+Cy=0
where y=transpose(y1 y2)
A=(1 0
0 1)
B=(0 1
1 0)
C=(1 1
1 1)

May someone give me a book name?:smile:
 
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but can't you make a second order diff eq into a sysytem by letting v=y'?
 
algebrat said:
but can't you make a second order diff eq into a sysytem by letting v=y'?

um...then what is y?
 
If you just want a book, Strogatz Nonlinear Dynamics and Chaos is very good.
this links supports PF

It's mainly a book on systems of ODEs and explains what algebrat mentioned.
 

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