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Problem 23

Nonlinear Spring. The Duffing equation $$ y^{\p…

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Problem 22

Oscillations and Nonlinear Equations. For the initial
value problem
$$\begin{array}{l}{x^{\prime \prime \prime}+(0.1)\left(1-x^{2}\right) x^{\prime}+x=0} \\ {x(0)=x_{0}, \quad x^{\prime}(0)=0}\end{array}$$
use the vectorized Runge-Kutta algorithm with $h=0.02$
to illustrate that as $t$ increases from 0 to 20, the solution
$x$ exhibits damped oscillations when $x_{0}=1,$ whereas $x$
exhibits expanding oscillations when $x_{0}=2.1$

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