Q1) One of the following is correct for functions the f(x) = 1, g(x)=x³ and h(x) In(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 -2 Q2) L-1 H a)-2cosht 343 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) ex 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 + ₂x³ S - ©Y(x) =GẮ+6x3 d) y(x) = c₂x + ₂x³ Q6) Evaluate (2 e-2t sin4t -0.5 cos3t): 8 S 8 5 a) - b) (-2)²+16 25¹+18 (s+2)² +16 d) c) 2s² +18 (+2)+16 25³ +18 Q7) The general solution of y"-4y' +9y = 0, is: a) y(t)=ce²t 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) = b)y(t) = cet cos(√5 t) + ₂'sin (√5t) d) y(t) = ce cos(5 t) + cefsin (5 t) is: . (3+2)(5-2) a) f(t) == +² c) f(t) ==e+ B b) f(t)=e+e-2 d)f (t) ==e7+²e²t -2t Q9) The solution of y" + y'= 0 by using power series method, is: a) y(x) = a + a₁ (1-=- +-+- b) y(x) = 31 51 c) y(x) = a + a₁(x-+-+ d)y(x) 31 41 51 - (8-2)² +16 = a₁ + a₂ ( 1 + = = =+ ) = a₁ + a₂(x + = = = =+ II 51
Q1) One of the following is correct for functions the f(x) = 1, g(x)=x³ and h(x) In(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 -2 Q2) L-1 H a)-2cosht 343 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) ex 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 + ₂x³ S - ©Y(x) =GẮ+6x3 d) y(x) = c₂x + ₂x³ Q6) Evaluate (2 e-2t sin4t -0.5 cos3t): 8 S 8 5 a) - b) (-2)²+16 25¹+18 (s+2)² +16 d) c) 2s² +18 (+2)+16 25³ +18 Q7) The general solution of y"-4y' +9y = 0, is: a) y(t)=ce²t 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) = b)y(t) = cet cos(√5 t) + ₂'sin (√5t) d) y(t) = ce cos(5 t) + cefsin (5 t) is: . (3+2)(5-2) a) f(t) == +² c) f(t) ==e+ B b) f(t)=e+e-2 d)f (t) ==e7+²e²t -2t Q9) The solution of y" + y'= 0 by using power series method, is: a) y(x) = a + a₁ (1-=- +-+- b) y(x) = 31 51 c) y(x) = a + a₁(x-+-+ d)y(x) 31 41 51 - (8-2)² +16 = a₁ + a₂ ( 1 + = = =+ ) = a₁ + a₂(x + = = = =+ II 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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