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4. Solve the initial value problem y" - y = 0, y(0)=3, y'(0)=5 (a) y =...
5. Solve the initial value problem y” + 2y' + y = 0, y(0=1, y'(1)=0 (a) y=e* +4xe* (b) y= e^ +3xe 1 (c) y= e^ +2xe" (d) y= " + xe" (e) y=e* (f) y= e" - xe " (g) y=e* - 2xe* (h) y=-e" -3xe *
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...
Solve the initial value problem y" – 3y' + 2y = e3r, y(0) = 2, y'(0) = -1. (a) y(x) = 40-1 – 4e2+ 2e 32 (b) y(x) = 1 e?' – 4e-2x + £230 (c) y(x) = 40-1 – 4e-2x + 3e3x (d) y(x) = 40" – 4e2x + e3r Select one: a с b d
Consider the initial value problem s' (t) = Ayt), y(0) = 13): where A is a 2 x 2 matrix and y= Yi , 1. You are given that the eigenvalues and eigenvectors of A are Ly2 11 = -1, 41 = and 12 = -4, 92 = 0,21 The solution of the initial value problem is y1 = -5e-t+6e-4t y2 = 3e-t - 3e-4t yy = -5e-4t +6e-t y2 = 3e-4t - 3e-t = -3et+4e-4t = 2e-t – 2e-4t...
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Solve the initial-value problem. y" (0) =-1 y(0) = 2, y'(0) = 2, у",-2y" + y,-xe* + 5,
1) y'' -2y'+y=xE^x, y(0)=y'(0)=0 Solve the initial value problem using the Laplace transform. y" – 2y + y = xe*, y(0) = y'(0) =
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
5. Solve the initial value problem, y"+y' - by = 4e* with y(0) = 1 and y'(0) = 1
5. Solve the initial value problem y" + 4y = 2 + 3e", y(0) = 0, y(0) = 2.