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
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˙=17y(1−y7) such that y(0)=14y(0)=14. Determine limt→∞y(t)limt→∞y(t) without finding y(t) explicitly.
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
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.
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular point atx 0. The indicial equation for x 0 is 2+ 0 r+ with roots (in increasing order) r and r2 Find the indicated terms of the following series solutions of the differential equation: x4. (a) y =x (9+ x+ (b) y x(7+ The closed form of solution (a) is y
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has...
(1 point) Consider the initial value problem my + cy + ky = F(t), y0 = 0, y (0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is (20 if 0 <t< /2, F(t) = 30...
y' = f(y, t), y(t0) = y0. (i) what conditions guaranteeing a unique solution to the nonlinear initial value problem (ii) After checking the conditions, state what the theorem predicts for the initial value problem y' = (-x2 )/y , y(1) = 0. (iii) Solve the above initial value problem and find two distinct solutions (iv) Explain if results in (iii) and in (ii) contradict each other
Q2: choose the right answer: 1. Determine whether y = e3t is a solution of ý – 49 – 4y + 16 y = 0 ? ( a. y is not a solution b. y is a solution ) if you selected (a.), write only y = .... as the right solution. 2. Determine C, and C so that y(x) = Cje2x + Czet + 2 sin x will satisfy the conditions y(0) = 0 and y'(0) = 1? (a.{C=1,C=-1}...
Given the initial-value problem y'=2-2tyt2+1, 0 ≤t≤1, y0=1 With exact solution yt= 2t+1t2+1 Using MATLAB use Euler’s method with h = 0.1 to approximate the solution of y