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(iv) The trial form y,(x) for the differential equation y" + 2y' + 2y = cos(x) is... (a) yp(x) = Acos(x) + B sin(x) (b) yp(x) = Ax cos(x) + Ba sin(x) (c) yp(x) = Ae- cos(x) + Be sin(r) (d) yp(x) = Axe- cos(x)+Bre- sin(x) %3D

(iv) The trial form y,(x) for the differential equation y" + 2y' + 2y = cos(x) is... (a) yp(x) = Acos(x) + B sin(x) (b) yp(x) = Ax cos(x) + Ba sin(x) (c) yp(x) = Ae- cos(x) + Be sin(r) (d) yp(x) = Axe- cos(x)+Bre- sin(x) %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q4

(i) The first-order differential equation y+y=x 1s... (a) linear. (b) separable (c) power homogeneous (d) Bernoulli 1 y = (ii) The integrating factor for the linear differential equation y + is... 1 (a) μ(x) %3D In() (c) (1) = Ja 1 (b) д() 2 (d) µ(1) = VI (m) f the second-order differential equation y+2u +2u = g(x) has the particular solution y,(x) = xe-, then... (a) g(x) = e- (b) g(x) = xe- (c) g(x) = x²e-z (d) g(x) = 0 (iv) The trial form y,(x) for the differential equation y" + 2y + 2y = cos(T) 1s... (a) Yp(x) = A cos(x) + B sin(x) (b) Yp(T) = Ax cos(x) + Bx sin(x) (c) yp(x) = Ae- cos(x) + Be- sin(x) (d) yp(x) = Are- cos(r)+Bxe- sin(z) (v) The pendulum/spring model ma" + 4x' + x = 0 is critically damped if... (а) т 3D 0. (b) т — 1 (с) т 3 4 (d) m = 16 (vi) If A is a 2 x 5 matrix and B is an 5 x 2 matrix then AB + BA is... (a) a 2 x 2 matrix (c) a 2 x 5 matrix (b) a 5 x 5 matrix (d) undefined [] (vii) The eigenvalues of A = are... (a) d = A2 = 0 (b) A = A, = 1 (c) A1 = 0, 2 = 1 (d) A1 = 0, 12 = 2
Transcribed Image Text:(i) The first-order differential equation y+y=x 1s... (a) linear. (b) separable (c) power homogeneous (d) Bernoulli 1 y = (ii) The integrating factor for the linear differential equation y + is... 1 (a) μ(x) %3D In() (c) (1) = Ja 1 (b) д() 2 (d) µ(1) = VI (m) f the second-order differential equation y+2u +2u = g(x) has the particular solution y,(x) = xe-, then... (a) g(x) = e- (b) g(x) = xe- (c) g(x) = x²e-z (d) g(x) = 0 (iv) The trial form y,(x) for the differential equation y" + 2y + 2y = cos(T) 1s... (a) Yp(x) = A cos(x) + B sin(x) (b) Yp(T) = Ax cos(x) + Bx sin(x) (c) yp(x) = Ae- cos(x) + Be- sin(x) (d) yp(x) = Are- cos(r)+Bxe- sin(z) (v) The pendulum/spring model ma" + 4x' + x = 0 is critically damped if... (а) т 3D 0. (b) т — 1 (с) т 3 4 (d) m = 16 (vi) If A is a 2 x 5 matrix and B is an 5 x 2 matrix then AB + BA is... (a) a 2 x 2 matrix (c) a 2 x 5 matrix (b) a 5 x 5 matrix (d) undefined [] (vii) The eigenvalues of A = are... (a) d = A2 = 0 (b) A = A, = 1 (c) A1 = 0, 2 = 1 (d) A1 = 0, 12 = 2
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