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a) e-3x b) ex ©e. d) Q4) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u'-6u = -6 c) u' - 6u = 6 d) u' + 6u = 6 lution of 2x2y" + 3xy'-15y = 0, is:

a) e-3x b) ex ©e. d) Q4) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u'-6u = -6 c) u' - 6u = 6 d) u' + 6u = 6 lution of 2x2y" + 3xy'-15y = 0, is:

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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SOLVE Q4
Q1) One of the following is correct for functions the f(x) = 1, g(x)= x³ and h(x) M a) f(x), g(x) and h(x) are linearly dependent c) W (f(x), g(x), h(x)) = 0 b) f(x), g(x) and h(x) are linearly independent d) W(f(x), g(x), h(x)) = 9 Q2) L-1 -2s 2+3 H a) -2coshnt b)-2sinhnt c)-2cosnt d)-2sinnt Q3) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, is: a) e-3x b) ei* d) e³x Q4) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u' - 6u = -6 c) u'-6u = 6 d) u' + 6u = 6 Q5) The general solution of 2x2y" + 3xy'-15y = 0, is: a) y(x) = ₂x² + ₂x³ b) y(x) = ₂x + ₂x-3 c) y(x) = c₁x² + ₂x-3 d) y(x) = c₁x + ₂x³ Q6) Evaluate L (2 e-2 sin4t -0.5 cos3t): 8 S a) (s+2)² +16 b) c) (8+2)² +16 23²418 (5-2)2+16 25² +18 2s² +18 (s-2)² +16 Q7) The general solution of y"-4y' +9y = 0, is: a) y(t)=ce²t cos(5 t) + c₂e²tsin (5 t) c)y(t) = cet cos(√5 t) + c₂e²t sin (√5 t) Q8) The inverse Laplace transform of H(s): b)y(t) = ce cos(√5 t) + c₂e¹sin (√5t) d) y(t) = ce cos(5 t) + cesin (5 t) 1 = is: . (35+2)(5-2) a) f(t) ==e+e²t b) f(t) ==e. 8 c) f(t) ==e+e-2t d)f(t) ==e. +²e²t Q9) The solution of y" + y'= 0 by using power series method, is: a) y(x) = ao + a₁ (1- 11 b) y(x) = a + a₁(1+ 21 31 41 St 21 c) y(x) = a₁ + a₁(x-+ d)y(x) = a + a₂(x + == 51 - e-2t 1 2s² +18 + + ii 41 41 51 ++ + ...)
Transcribed Image Text:Q1) One of the following is correct for functions the f(x) = 1, g(x)= x³ and h(x) M a) f(x), g(x) and h(x) are linearly dependent c) W (f(x), g(x), h(x)) = 0 b) f(x), g(x) and h(x) are linearly independent d) W(f(x), g(x), h(x)) = 9 Q2) L-1 -2s 2+3 H a) -2coshnt b)-2sinhnt c)-2cosnt d)-2sinnt Q3) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, is: a) e-3x b) ei* d) e³x Q4) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u' - 6u = -6 c) u'-6u = 6 d) u' + 6u = 6 Q5) The general solution of 2x2y" + 3xy'-15y = 0, is: a) y(x) = ₂x² + ₂x³ b) y(x) = ₂x + ₂x-3 c) y(x) = c₁x² + ₂x-3 d) y(x) = c₁x + ₂x³ Q6) Evaluate L (2 e-2 sin4t -0.5 cos3t): 8 S a) (s+2)² +16 b) c) (8+2)² +16 23²418 (5-2)2+16 25² +18 2s² +18 (s-2)² +16 Q7) The general solution of y"-4y' +9y = 0, is: a) y(t)=ce²t cos(5 t) + c₂e²tsin (5 t) c)y(t) = cet cos(√5 t) + c₂e²t sin (√5 t) Q8) The inverse Laplace transform of H(s): b)y(t) = ce cos(√5 t) + c₂e¹sin (√5t) d) y(t) = ce cos(5 t) + cesin (5 t) 1 = is: . (35+2)(5-2) a) f(t) ==e+e²t b) f(t) ==e. 8 c) f(t) ==e+e-2t d)f(t) ==e. +²e²t Q9) The solution of y" + y'= 0 by using power series method, is: a) y(x) = ao + a₁ (1- 11 b) y(x) = a + a₁(1+ 21 31 41 St 21 c) y(x) = a₁ + a₁(x-+ d)y(x) = a + a₂(x + == 51 - e-2t 1 2s² +18 + + ii 41 41 51 ++ + ...)
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