2. Consider the IVP /" -+13y-6(t-2), (o)-o,)-1 a. Solve the IVP. b. Find the exact value...
1. Consider the IVP y = 1 - 100(y-t), y(0) = 0.5. (a) Find the exact solution. (b) Use the Forward Euler, Heun, and Backward Euler methods to find approximate solu- tions ont € 0, 0.5], using h = 0.25. Plot all four solutions (exact and three approxima- tions) on the same graph. (c) Maple's approximation is plotted, along with the direction field, in Figure 1. Use it, and the exact solution, to explain the behaviours observed in your numerical...
1.a. b. c. Solve the IVP 2 [:] = [3 =:] [:] []=[3] ņ Find e At where 2 5 A = -2 -4 Solve the IVP (21-1 -3) M (O)-() x(0) I g(0)
Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve this IVP by using the Method of Undetermined Coefficients (MUC). 2. Solve this IVP by using the Variation of Parameters Method (VOP). Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve...
pls do all questions. thanx 1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...
Exercise 6 Solve the IVP y" +54 + 6y = u(t - 1) +(t – 2), y(0) = 0, y'(0) = 1
a. b. Solve the IVP -5 3 [= il (x1+[ 6te *) (O)=(-1) -3 Solve the IVP 79 [] = [-* ?] [?]+[6] [70] = [4] 1 0
Name: ID number:_ Q1. Test for exactness. If exact solve the ODE or the IVP. If not find an integrating factor, then solve. b. (x2 + y*)dx-2xdy = 0, y(1) = 0.
Solve the IVP 1 (31= [ -> ] (3) [6**) (O)= [-] +
Solve the IVP using laplace transformation y”+3y=(t-2)u(t-1) y(0)=-1 y’(0)=2 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1
Consider the IVP, 1. Apply the FEUT to show that a solution exists. 2. Use the Runge-Kutta method with various step-sizes to estimate the maximum t-value, t=t∗>0, for which the solution is defined on the interval [0,t∗). Include a few representative graphs with your submission, but not the lists of points. 3. Find the exact solution to the IVP and solve for t∗ analytically. How close was your approximation from the previous question? 4. The Runge-Kutta method continues to give...