Question: A Consider the nonlinear model [dot{x}+a x|x|=e^{-2 t / 3} sin t, quad x(0)=0.3, quad 0 leq t leq 15] where (a) is a parameter.
A Consider the nonlinear model
\[dot{x}+a x|x|=e^{-2 t / 3} \sin t, \quad x(0)=0.3, \quad 0 \leq t \leq 15\]
where \(a\) is a parameter. Use the RK4 method to plot the response \(x(t)\) for \(a=0.2,0.8,1.5\) versus \(t\) in the same graph.
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