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

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.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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