For the system 会-(1)-() dx 5 -37 291 x + dt 55 determine the critical point x = x", and then classify its type and examine its stability by making the transformation x = x° + u. The critical point is (?, ?) It is a stable spiral
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- determine the critical point x = x0, and then classify its type and examine its stability by making the transformation x = x0 + u. 13.(0−βδ0)+(α−γ);α,β,γ,δ>0Q.2 Check whether the following system given by its characteristic equation is stable or not and shows the location of roots on the s-planeConsider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. Find the general form of r(t), the position of the particle, as a function of time t, (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot).