(i) The first-order differential equation y + y = x is... (a) linear. (b) separable (c) power homogeneous (d) Bernoulli 1 (ii) The integrating factor for the linear differential equation y +: is... (a) µ(x) = In(x) (c) µ(1) =- 1 (b) µ(x) = (d) µ(x) = VE %3D (iii) If the second-order differential equation +2v +2y = g(1) has the particulal solution y,(x) = xe-², then... %3D (a) g(x) = e-z (b) g(x) = xe- (c) g(x) = x²e-z (d) g(x) = 0 %3D (iv) The trial form y,(x) for the differential equation y" + 2y + 2y = cos(I) 15... (a) yp(x) = Acos(x) + B sin(x) (b) yp(x) = Ax cos(x) + Bx sin(x) (c) yp(x) = Ae- cos(x) + Be- sin(r) (d) yp(x) = Axe- cos(x)+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 %3D (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) а 5 х 5 matrix (c) a 2 x 5 matrix (d) undefined (vii) The eigenvalues of A= are... (a) A1 = 12 = 0 (b) A = A2 = 1 (c) A1 = 0, 22 = 1 (d) A1 = 0, 12 = 2 %3D %3D %3D %3D
(i) The first-order differential equation y + y = x is... (a) linear. (b) separable (c) power homogeneous (d) Bernoulli 1 (ii) The integrating factor for the linear differential equation y +: is... (a) µ(x) = In(x) (c) µ(1) =- 1 (b) µ(x) = (d) µ(x) = VE %3D (iii) If the second-order differential equation +2v +2y = g(1) has the particulal solution y,(x) = xe-², then... %3D (a) g(x) = e-z (b) g(x) = xe- (c) g(x) = x²e-z (d) g(x) = 0 %3D (iv) The trial form y,(x) for the differential equation y" + 2y + 2y = cos(I) 15... (a) yp(x) = Acos(x) + B sin(x) (b) yp(x) = Ax cos(x) + Bx sin(x) (c) yp(x) = Ae- cos(x) + Be- sin(r) (d) yp(x) = Axe- cos(x)+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 %3D (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) а 5 х 5 matrix (c) a 2 x 5 matrix (d) undefined (vii) The eigenvalues of A= are... (a) A1 = 12 = 0 (b) A = A2 = 1 (c) A1 = 0, 22 = 1 (d) A1 = 0, 12 = 2 %3D %3D %3D %3D
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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