+2y" -y'-2y = 0, is: Q10) The general solution of y" a) y(x) = c₂e²x + ₂x + c₂e* c) y(x) = c₂e²x + c₂e* Q11) L(y") = b) y(x) = c₂e-2 +₂e-* d) y(x) = c₂e-²x + c₂e²+G₂e™* a) s² L(y(x)) + sy(0) - y'(0) c) s² L(y(x))-sy(0)-y'(0) b) s² L(y(x))+ sy(0) + y'(0) of f(t),t> 0, is: d) s² L(y(x))-sy(0) + y'(0) Q12) The kernel of the Laplace transform b) e-t c) est Q13) Evaluate (e-t sin4t): 842 a) 3²+45+20 b) 142 x² +8+20 d) +8+20 Q14) If the power series method was used to solve the following ODE. (x-0.5)y" x+0.5 G y' + (x²-1) y = 0.xo = 0. Then the interval of convergence, is: b) (-1,1) c) (0,00) (9) Q15) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0,0,0,2+51,2-5i, then the general solutiom of this ODE, is: a) c₂ + ₂x + ₂x² +ex [Acos(x) + Bsin(x)] b) c₂ +₂x+3x²+e5x[Acos(2x) + Bsin(2x)] c) c₂x+c₂x² + 3x³ + e*[Acos(5x) + Bsin(5x)] d) G₂ +G₂x + ₂x² + ²x [Acos(5x) + Bsin(5x)] Q16) Combine the following power series expressions into a single power series. Σ(n+1)(x-2)-1 +Eon(x - 2)" a) (2n + 1)(x)" b) So(2n + 2)(x)" c) Eno(2n + 2)(x - 2)" d) (2n+1)(x-2)" Q17) If you know that the radius of convergent of the series method for the ODE y"+y+z=0, x=2 is 5. Find the value for b, (b<0): (a)-5 (b)-3 (c)-2 d)-8 Q18) The formula of the particular solution yp of y) + 4y" = 3 sin(2t) - 5cos2t, is: a) yp= Asin(t) + Bcos(t) b) yp= Atsin(t) + Btcos(t) c) y = Asin(2t) + Bcos(2t) d) y, Atsin(2t) + Btcos(2t) Q19) est dt = a) b) 0 c)=- d) 00 Q20) The singular point (s) of (x + 1) y' + x²y = 0, is (are): a) 0,1 b) 0,-1 c) 0 d)-1 1 = Q21) L-1 a) cosht - 1 s(5²-1) Q22) Given that y₁ (t) = t¹ is solution for b) ti b) 1-cosht c) (cosh2t - 1) 2t2y" +ty' - 3y = 0,t> 0, then y₂ (t) is: a)t c) ti d) ti 1 Q23) -3tsinst 5 ¹(-32+25) = b) est sin3t 5 c) d). e-at sin3t 5 a) Q24) The general solution for y' = 6y²x, is: a) == 3x² + c b) ² = x² + c c) =² = 3x² + c d) == x² + c y Q25) The form of a particular solution of y"-4y' - 12y = sin(2t), is: a) y(t) = A sin(2t) b) y(t) = A cos(t) c) y(t) = A cos(2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) d) (1-cosh2t) estsinst 5
+2y" -y'-2y = 0, is: Q10) The general solution of y" a) y(x) = c₂e²x + ₂x + c₂e* c) y(x) = c₂e²x + c₂e* Q11) L(y") = b) y(x) = c₂e-2 +₂e-* d) y(x) = c₂e-²x + c₂e²+G₂e™* a) s² L(y(x)) + sy(0) - y'(0) c) s² L(y(x))-sy(0)-y'(0) b) s² L(y(x))+ sy(0) + y'(0) of f(t),t> 0, is: d) s² L(y(x))-sy(0) + y'(0) Q12) The kernel of the Laplace transform b) e-t c) est Q13) Evaluate (e-t sin4t): 842 a) 3²+45+20 b) 142 x² +8+20 d) +8+20 Q14) If the power series method was used to solve the following ODE. (x-0.5)y" x+0.5 G y' + (x²-1) y = 0.xo = 0. Then the interval of convergence, is: b) (-1,1) c) (0,00) (9) Q15) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0,0,0,2+51,2-5i, then the general solutiom of this ODE, is: a) c₂ + ₂x + ₂x² +ex [Acos(x) + Bsin(x)] b) c₂ +₂x+3x²+e5x[Acos(2x) + Bsin(2x)] c) c₂x+c₂x² + 3x³ + e*[Acos(5x) + Bsin(5x)] d) G₂ +G₂x + ₂x² + ²x [Acos(5x) + Bsin(5x)] Q16) Combine the following power series expressions into a single power series. Σ(n+1)(x-2)-1 +Eon(x - 2)" a) (2n + 1)(x)" b) So(2n + 2)(x)" c) Eno(2n + 2)(x - 2)" d) (2n+1)(x-2)" Q17) If you know that the radius of convergent of the series method for the ODE y"+y+z=0, x=2 is 5. Find the value for b, (b<0): (a)-5 (b)-3 (c)-2 d)-8 Q18) The formula of the particular solution yp of y) + 4y" = 3 sin(2t) - 5cos2t, is: a) yp= Asin(t) + Bcos(t) b) yp= Atsin(t) + Btcos(t) c) y = Asin(2t) + Bcos(2t) d) y, Atsin(2t) + Btcos(2t) Q19) est dt = a) b) 0 c)=- d) 00 Q20) The singular point (s) of (x + 1) y' + x²y = 0, is (are): a) 0,1 b) 0,-1 c) 0 d)-1 1 = Q21) L-1 a) cosht - 1 s(5²-1) Q22) Given that y₁ (t) = t¹ is solution for b) ti b) 1-cosht c) (cosh2t - 1) 2t2y" +ty' - 3y = 0,t> 0, then y₂ (t) is: a)t c) ti d) ti 1 Q23) -3tsinst 5 ¹(-32+25) = b) est sin3t 5 c) d). e-at sin3t 5 a) Q24) The general solution for y' = 6y²x, is: a) == 3x² + c b) ² = x² + c c) =² = 3x² + c d) == x² + c y Q25) The form of a particular solution of y"-4y' - 12y = sin(2t), is: a) y(t) = A sin(2t) b) y(t) = A cos(t) c) y(t) = A cos(2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) d) (1-cosh2t) estsinst 5
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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