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Q10) The general solution of y+2y"-y-2y = 0, is: a) y(x) =ce²+₂*+* b) y(x) = c₂e-+6₂8 Q11) L(y") =

Q10) The general solution of y+2y"-y-2y = 0, is: a) y(x) =ce²+₂*+* b) y(x) = c₂e-+6₂8 Q11) L(y") =

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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please solve question differential equations 10

Q10) The general solution of y" +2y"-y-2y = 0, is: a) y(x)=ce² +₂e^*+₂* c) x(x) = ₁² + get Q11) L(y") = b) y(x) = c₂e-x+ G₂e" a) s Ly(x))+ sy(0) - y'(0) c) s³ L(y(x)) -sy(0)-y'(0) Q12) The kernel of the Laplace transform b) ent b) s²L(y(x))+ sy(0) + y'(0) of f(t).t> 0, is: d)s L(y(x))-sy(0) + y (0) c) est Q13) Evaluate (e-2 sin4t): d) e 342 342 2³+0+20 Q14) If the power series method was used to solve the following ODE. (x-0.5)y" 240.5 y' + (x²-1) y=0, x=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+St.2-Si. then the general solution of this ODE.is: a) c₂ + ₂x + ₂x² + x[Acos(x) + Bsin(x)] b) c₂ + ₂x + ₂x² + e[Acos(2x) + Bsin(2x)] c) G₁₂x+₂x² + ₂x + e[Acos(5x) + Bsin(5x)] d) G+qx+g₂x² +eAcos(5x) + Bsin(5x)] Q16) Combine the following power series expressions into a single power series, (+1)(x-2)-1 + (x-2)" b) (2n + 1)(x)" (2n+2)(x)" (2n+2)(x-2)" c) d) (2n+1)(x-2)" Q17) If you know that the radius of convergent of the series method for the ODE y"+y+=0, x=2 is S. Find the value for b. (b<0): d)-8 (@)-5 (b)-3 (c)-2 Q18) The formula of the particular solution y, of y(+4y"=3 sin(2t) - 5cos2t, is: a) y = Asin(t) + Bcos(t) c) y = Asin(2t) + Bcos(2t) b) y= Atsin(t) + Btcos(t) d) y, Atsin(2t) + Btcos(2t) b) 0 c) = d) 00 Q19)dt = 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) ¹ ( (5) a) cosht-1 Q22) Given that y, (t) = t¹ is solution for b) ti b) 1-cosht c) (cosh2t - 1) 2ty"+ty'-3y = 0,t> 0, then y₂ (t) is: d) t -inst sin3t Q23) £¹)= a) b) est sin3t 5 c) d) 5 5 Q24) The general solution for y' = 6y²x, is: = 3x² + c b) x² + c c) == 3x² + c d)=x² + c 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) + 8 sin(2t) d) y, (t) = A cos(t) + B sin(t) d)/(1-cosh2t) etsinst 5
Transcribed Image Text:Q10) The general solution of y" +2y"-y-2y = 0, is: a) y(x)=ce² +₂e^*+₂* c) x(x) = ₁² + get Q11) L(y") = b) y(x) = c₂e-x+ G₂e" a) s Ly(x))+ sy(0) - y'(0) c) s³ L(y(x)) -sy(0)-y'(0) Q12) The kernel of the Laplace transform b) ent b) s²L(y(x))+ sy(0) + y'(0) of f(t).t> 0, is: d)s L(y(x))-sy(0) + y (0) c) est Q13) Evaluate (e-2 sin4t): d) e 342 342 2³+0+20 Q14) If the power series method was used to solve the following ODE. (x-0.5)y" 240.5 y' + (x²-1) y=0, x=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+St.2-Si. then the general solution of this ODE.is: a) c₂ + ₂x + ₂x² + x[Acos(x) + Bsin(x)] b) c₂ + ₂x + ₂x² + e[Acos(2x) + Bsin(2x)] c) G₁₂x+₂x² + ₂x + e[Acos(5x) + Bsin(5x)] d) G+qx+g₂x² +eAcos(5x) + Bsin(5x)] Q16) Combine the following power series expressions into a single power series, (+1)(x-2)-1 + (x-2)" b) (2n + 1)(x)" (2n+2)(x)" (2n+2)(x-2)" c) d) (2n+1)(x-2)" Q17) If you know that the radius of convergent of the series method for the ODE y"+y+=0, x=2 is S. Find the value for b. (b<0): d)-8 (@)-5 (b)-3 (c)-2 Q18) The formula of the particular solution y, of y(+4y"=3 sin(2t) - 5cos2t, is: a) y = Asin(t) + Bcos(t) c) y = Asin(2t) + Bcos(2t) b) y= Atsin(t) + Btcos(t) d) y, Atsin(2t) + Btcos(2t) b) 0 c) = d) 00 Q19)dt = 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) ¹ ( (5) a) cosht-1 Q22) Given that y, (t) = t¹ is solution for b) ti b) 1-cosht c) (cosh2t - 1) 2ty"+ty'-3y = 0,t> 0, then y₂ (t) is: d) t -inst sin3t Q23) £¹)= a) b) est sin3t 5 c) d) 5 5 Q24) The general solution for y' = 6y²x, is: = 3x² + c b) x² + c c) == 3x² + c d)=x² + c 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) + 8 sin(2t) d) y, (t) = A cos(t) + B sin(t) d)/(1-cosh2t) etsinst 5
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