Q1) One of the following is correct for functions the f(x) = 1 g(x)= x³ and h(x)= 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 -2s Q2) L-1 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) ex 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) = c₂x² + ₂x³ b) y(x) = ₂x + ₂x-3 c) y(x) = c₂x² + ₂x-3 d) y(x) = ₂x + ₂x³ Q6) Evaluate L (2e-2 sin4t -0.5 cos3t): 8 8 a) (s+2)² +16 25²+18 b) (8-2)2+16 28³+18 c)(8+2)³+16 25³ +18 Q7) The general solution of y"-4y' +9y = 0, is: a) y(t) = c₁e²t cos(5 t) + c₂e²t sin (5 t) c)y(t) = c₂e²t cos(√5 t) + c₂e²sin (√5 t) Q8) The inverse Laplace transform of H(s) = a) f(t)=e+ b)y(t) = cet cos(√5 t) + c₂esin (√5t) d) y(t) = ce cos(5 t) + ₂e sin (5 t) 1 is: * 1 2t (35+2)(x-2) b) f(t) ==e7² +²e-2t 8 c) f(t) ==e+e-2t d)f(t) ==e7+²e²t Q9) The solution of y"+y' = 0 by using power series method, is: a) y(x) = a + a₁ (1-+ 11 31 41 51 b) y(x) = a + a₂ (1+- d)y(x) = a + a₂(x + == c) y(x) = a + a₁(x-+ x4 + 51 d) (5-2)²+1625²+18 ++ 11 51 +)
Q1) One of the following is correct for functions the f(x) = 1 g(x)= x³ and h(x)= 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 -2s Q2) L-1 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) ex 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) = c₂x² + ₂x³ b) y(x) = ₂x + ₂x-3 c) y(x) = c₂x² + ₂x-3 d) y(x) = ₂x + ₂x³ Q6) Evaluate L (2e-2 sin4t -0.5 cos3t): 8 8 a) (s+2)² +16 25²+18 b) (8-2)2+16 28³+18 c)(8+2)³+16 25³ +18 Q7) The general solution of y"-4y' +9y = 0, is: a) y(t) = c₁e²t cos(5 t) + c₂e²t sin (5 t) c)y(t) = c₂e²t cos(√5 t) + c₂e²sin (√5 t) Q8) The inverse Laplace transform of H(s) = a) f(t)=e+ b)y(t) = cet cos(√5 t) + c₂esin (√5t) d) y(t) = ce cos(5 t) + ₂e sin (5 t) 1 is: * 1 2t (35+2)(x-2) b) f(t) ==e7² +²e-2t 8 c) f(t) ==e+e-2t d)f(t) ==e7+²e²t Q9) The solution of y"+y' = 0 by using power series method, is: a) y(x) = a + a₁ (1-+ 11 31 41 51 b) y(x) = a + a₂ (1+- d)y(x) = a + a₂(x + == c) y(x) = a + a₁(x-+ x4 + 51 d) (5-2)²+1625²+18 ++ 11 51 +)
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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