Consider the initial value problem s' (t) = Ayt), y(0) = 13): where A is a...
4. Solve the initial value problem y" - y = 0, y(0)=3, y'(0)=5 (a) y = 4e - (b) y = 5e-2 (c) y = 60"-3e (d) y = 7e-4e (e) y = 2e +e (f) y=e' +2e (g) y = 3e* (h) y=-e +4e- 5. Solve the initial value problem y" + 2y + y = 0, y(0-1, y (1)=0 (a) y=e"* + 4xe (b) y= e' +3xe" (c) y= + 2xe * (d) y= e^ + xe" (e)...
6. Solve the initial value problem y" + y = 0, y(0)=0, y'0=1 (a) -COS X (b) -sin x (c) -sin x + cos x (d) -sin x COS X (e) COS X (f) sin x (g) sin x-COS X (h) sin x + cos x 7. Find a particular solution yn of the differential equation (using the method of undetermined coefficients): y + y =p2 (a) 2e (b) 3e (c) 4e: (d) 6e (e) 2/2 (f) e2/3 (g) e2/4...
(1 point) Let 9 -4 15 -7' 6e3' +2e-t 9e3' +5e' y,(t) a. Show that yi(t) is a solution to the system y - Py by evaluating derivatives and the matrix product 9 -41+ 15 -7 yi(t) Enter your answers in terms of the variable t b. Show that y2(t) is a solution to the systemy - Py by evaluating derivatives and the matrix product 9 -4:- 15 -7 y2(t) - y2(t) Enter your answers in terms of the variable...
(1 point) Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 11 = -3i .. , , and 12 = -3i , 01 (b) Solve the initial value problem. Give your solution in real form. X(t) = Use the phase plotter pplane9.m in MATLAB to answer the following question. An ellipse with clockwise orientation 41. Describe the trajectory.
*Matlab code, please! only 1d
(a) 1. Apply the Euler’s Method with step size h = 1/4 to the initial value problem on [0, 1]. y1 = yi + y2 yí = -yi – 12 ya = - y1 + y2 on J y2 = yi – Y2 yı(0) = 1 yı(0) = 1 y2 (0) = 0 | Y2(0) = 0 y =-12 yí = yi + 3y2 ya = 2yı + 2y2 (d) yı(0) = 1 yi(0) =...
(1 point) Consider the Initial Value Problem xi(0) 6 = 10xi-4x2 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. ,V2- and 12 (b) Solve the initial value problem. Give your solution in real form x1F X2=
(1 point) Consider the Initial Value Problem xi(0) 6 = 10xi-4x2 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. ,V2- and 12 (b) Solve the initial value problem. Give your solution in real form x1F X2=
11. Solve the initial value problem y-4y 4t- 8e: y (0) = 2,y (0)= 5 (10 points) B. 2te-e-t+e A. te +2e 2 +2t-e -t +e C. 2te 2 -e -t+e D. te -2e 2
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(1 point) Consider the linear system 3'=[} }); a. Find the eigenvalues and eigenvectors for the coefficient matrix. EL and 12 = b. Find the real-valued solution to the initial value problem y! 3yı + 2y2, -5yı - 3y2, yı(O) = 5, y2(0) = -5. Use t as the independent variable in your answers. yi(t) = y2(t) =
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t), for the initial value problem with є * 0 and є is a small parameter.
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find...
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)