(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 (b) a 5 x 5 matrix (c) a 2 x 5 matrix (d) undefined

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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Q6

(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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