Solved: In 9 and 10 the given differential equation is a
Chapter 5, Problem 10E(choose chapter or problem)
In Problems 9 and 10 the given differential equation is a model of a damped nonlinear spring/mass system. Predict the behavior of each system as \(t \longrightarrow \infty\). For each equation use a numerical solver to obtain the solution curves satisfying the given initial conditions.
\(\frac{d^{2} x}{d t^{2}}+\frac{d x}{d t}+x-x^{3}=0\),
\(x(0)=0, x^{\prime}(0)=\frac{3}{2} ; \quad x(0)=-1, x^{\prime}(0)=1\)
Text Transcription:
t\infty
fracd^2xdt^2+fracdxdt+x-x^3=0
x(0)=0,x^prime(0)=frac32;x(0)=-1,x^prime(0)=1
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