Third order system Solve the differential equation x' + 11x" + 36x' + 26x = 26 with initial conditions x(0) = 2, x'(0) = 2, x"(0) = -2
question attached in photo but please read below
All of the answers to this take one of the following forms:
1. wextu(t) + yeztu(t) (where |x| ≥ |z|)
2. ext (w cos(zt) + y sin(zt)) u(t) (where z > 0) 3. ext(w+ytz)u(t)(wherez>0)
4. wextu(t)+ycos(t)u(t)+zsin(t)u(t)
5. u(t)+wextu(t)+yeztcos(t)u(t)
6. u(t)+wextu(t)+yeztsin(t)u(t)
where u(t) is the unit step function.
So your answers to each question will consist of 5 numbers: v (identifying which of the above forms 1–6 to use), followed by the numerical values of w, x, y and z. For a single decay, use form 1 (with y = z = 0). For an oscillation of constant magnitude, use form 2, with x = 0.
Unless otherwise specified, assume that the initial voltage across capacitors and the initial current through inductors is zero.
Step by step
Solved in 4 steps with 4 images
