Consider the spring model %D where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in x and y = x'. x' = y' = Write down your system when you have it correct, for use in the next three problems. Then find all critical points and enter them below, in order of increasing x coordinate. (x,y) = ( ); (x,y) = (| ); (x,y) = (| %3D For reference for the next three problems, write down your critical points after you've gotten them all right.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the spring model
х" — Зх + 3х3 %3D 0,
where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive).
Rewrite this as a system of first-order equations in x and y = x' .
x' =
y' =
Write down your system when you have it correct, for use in the next three problems.
Then find all critical points and enter them below, in order of increasing x coordinate.
(x,y) = ( .|): |x.y) = ( -[ ): (x.) = (|
);
For reference for the next three problems, write down your critical points after you've gotten them all right.
Transcribed Image Text:Consider the spring model х" — Зх + 3х3 %3D 0, where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in x and y = x' . x' = y' = Write down your system when you have it correct, for use in the next three problems. Then find all critical points and enter them below, in order of increasing x coordinate. (x,y) = ( .|): |x.y) = ( -[ ): (x.) = (| ); For reference for the next three problems, write down your critical points after you've gotten them all right.
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