Let y(t) be a solution of y˙=(1/5)y(1−y/5) such that y(0)=10 . Determine limt→∞y(t) without finding y(t) explicitly. limt→∞y(t) =
Let y(t) be a solution of y˙=(1/5)y(1−y/5) such that y(0)=10 . Determine limt→∞y(t) without finding y(t)...
Let y(t) be a solution of y˙=17y(1−y7) such that y(0)=14y(0)=14. Determine limt→∞y(t)limt→∞y(t) without finding y(t) explicitly.
Let y(t)y(t) be a solution of y˙=1/4y(1−y4) such that
y(0)=8.Determine limt→∞y(t) without finding y(t) explicitly.
9.0 Differential Eqns: Problem 6 Previous Problem List Next Results for this submission Answer Preview Entered The answer above is NOT correct. (1 point) Let y(t) be a solution of y such that y(0) 8. Determine lim y(t) without finding y(t explicitly. t oo lim y(t) t oo Preview My Answers Submit Answers Result ncorrect
(1 point) Let y(t) be a solution of ý = {y(1 – 3) such that y0) = 10. Determine lim y(t) without finding y(t) explicitly. ta lim Vt) = 1. 100
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
Determine the equilibrium, classify each equilibrium, draw a
phase line.
If y(0)=1 then lim y(t) = ?
If y(0)=2 then what is the solution y(t) =?
3/3-4y Let dt
3/3-4y Let dt
5. Let y E C2([0, T]; R), T > 0 satisfy y"(t) = 피t, y(0) = y'(0) = 0 e R. Use Picard-Lindelöf 1+t' to prove that a unique solution to the IVP exists for short time, as follows: (a) Let b E R2, A E M2 (R) . Show that any function g : R2 -R2.9(x) = Ax+b is Lipschitz. 1 mark (b) Transform the DE for y into a(t) Az(t) +b(t) for a suitable z, A, b. 2...
Let T(1, 0) – (1, 0) and T(0, 1) – (0, 2). (a) Determine T(x, y) for any (x, y). (b) Give a geometric description of T. o vertical sheer O vertical contraction vertical expansion horizontal expansion horizontal sheer horizontal contraction
use Matlab
y'=t, y0)=1, solution: y(t)=1+t/2 y' = 2(1 +1)y, y(0)=1, solution: y(t) = +24 v=5"y, y(0)=1, solution: y(t) = { y'=+/yº, y(0)=1, solution: y(t) = (31/4+1)1/3 For the IVPs above, make a log-log plot of the error of Runge-Kutta 4th order at t=1 as a function of h with h=0.1 x 2-k for 0 <k <5.
2 for y3+t -y. (0-1 uler's method to approximate a solution at t = 10 with a step size of 2 for y, 34 t-y, y(0) = 1. 1. Use E 2. Use Euler's method to approximate a solution at t = 10 with a step size of 1 for y' = 3 + t-y, y(0) = 1.
2 for y3+t -y. (0-1 uler's method to approximate a solution at t = 10 with a step size of 2 for...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...