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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8506d8a-21d7-4573-8755-d46c04285cac%2F72e93648-da9f-4f49-916e-5abeb3dd8f51%2Fm3huycd_processed.jpeg&w=3840&q=75)
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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