In Exercises 9–18, construct the general solution of x′ = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.
13. A =
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- Consider an oscillator satisfying the initial value problem (img1) If x1=u, x2=u′, write the equation in the form (img2) Find the general solution for PVI (img2)arrow_forwardConsider the IVP x00(t) + x = e−αx(t), x(0) = x0, x0(0) = 0, where x0 > 0,α > 0.(a) Solve the above IVP numerically and show the trajectories x(t) for various parametersx0 > 0 and α > 0.(b) Show that the above IVP admits only periodic solutions.arrow_forwardGive a counter example of a matrix that all eigenvalues are negative real part but every solution of differential equation x`=Ax satisfies |x(t)|<|x(s)| if t>s.arrow_forward
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