+8+20 +8+20 Q14) If the power series method was used to solve the following ODE. 1 (x-0.5)y" x+0.5 y' + (x²-1) y=0, x= 0. Then the interval of convergence, is: b) (-1,1) c) (0,00) Q15) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0.0.0.2+51 2 51
+8+20 +8+20 Q14) If the power series method was used to solve the following ODE. 1 (x-0.5)y" x+0.5 y' + (x²-1) y=0, x= 0. Then the interval of convergence, is: b) (-1,1) c) (0,00) Q15) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0.0.0.2+51 2 51
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
SOLVE Q14
![Q10) The general solution of y" +2y" -y'-2y = 0, is:
a) y(x) = c₂e²x+c₂e-² +₂ex
c) y(x) = c₂e²x + c₂e*
b) y(x) = c₂e-2x + c₂ex
Q11) L(y") =
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)
Q12) The kernel of the Laplace transform
b) e-t
b) s² L(y(x))+ sy(0) + y'(0)
of f(t),t> 0, is:
d) s² L(y(x))-sy(0) + y'(0)
c) est
Q13) Evaluate (e-t sin4t):
a)
842
b)
342
x² +8+20
d) +20
Q14) If the power series method was used to solve the following ODE.
(x-0.5)y"
x+0.5
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+51,2-51, then the general solutiom of this ODE, is:
a) c₂ + ₂x + ₂x² + e2x [Acos(x) + Bsin(x)]
b) c₂ + ₂x + ₂x² +e5x (Acos(2x) + Bsin(2x)]
c) c₂x + ₂x² + 3x³ + e*[Acos(5x) + Bsin(5x)]
d) G₂ + G₂x + C₂x² + 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) To(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+=0, x=2 is 5. Find the value for b, (b<0):
(a)-5
(b)-3
(c)-2
-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) y₂ = Asin(2t) + Bcos(2t)
d) y = Atsin(2t) + Btcos(2t)
Q19) est dt =
a)
b) 0
9)
d) ∞o
Q20) The singular point (s) of (x + 1) y' + x²y = 0, is (are):
a) 0,1
b) 0,-1
c) 0
d)-1
1
=
b) 1-cosht c) (cosh2t - 1) d) (1-cosh2t)
2t2y" +ty' - 3y = 0,t> 0, then y₂ (t) is:
Q21) L1
a) cosht - 1
s(s²-1)
Q22) Given that y₁ (t) = t¹ is solution for
a)t b) ti
Q23) L-1
c) ti
d) ta
estsinst
-atsinst
1
a)
b)
est sin3t
5
c)
e-at sin3t
5
d)
5
5
(s-3)2+25A
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7df285d-c30a-4214-bfbd-28e975c7e2db%2F437c5dc4-8f76-4a42-bebb-55099052b163%2Far3ejr7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q10) The general solution of y" +2y" -y'-2y = 0, is:
a) y(x) = c₂e²x+c₂e-² +₂ex
c) y(x) = c₂e²x + c₂e*
b) y(x) = c₂e-2x + c₂ex
Q11) L(y") =
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)
Q12) The kernel of the Laplace transform
b) e-t
b) s² L(y(x))+ sy(0) + y'(0)
of f(t),t> 0, is:
d) s² L(y(x))-sy(0) + y'(0)
c) est
Q13) Evaluate (e-t sin4t):
a)
842
b)
342
x² +8+20
d) +20
Q14) If the power series method was used to solve the following ODE.
(x-0.5)y"
x+0.5
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+51,2-51, then the general solutiom of this ODE, is:
a) c₂ + ₂x + ₂x² + e2x [Acos(x) + Bsin(x)]
b) c₂ + ₂x + ₂x² +e5x (Acos(2x) + Bsin(2x)]
c) c₂x + ₂x² + 3x³ + e*[Acos(5x) + Bsin(5x)]
d) G₂ + G₂x + C₂x² + 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) To(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+=0, x=2 is 5. Find the value for b, (b<0):
(a)-5
(b)-3
(c)-2
-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) y₂ = Asin(2t) + Bcos(2t)
d) y = Atsin(2t) + Btcos(2t)
Q19) est dt =
a)
b) 0
9)
d) ∞o
Q20) The singular point (s) of (x + 1) y' + x²y = 0, is (are):
a) 0,1
b) 0,-1
c) 0
d)-1
1
=
b) 1-cosht c) (cosh2t - 1) d) (1-cosh2t)
2t2y" +ty' - 3y = 0,t> 0, then y₂ (t) is:
Q21) L1
a) cosht - 1
s(s²-1)
Q22) Given that y₁ (t) = t¹ is solution for
a)t b) ti
Q23) L-1
c) ti
d) ta
estsinst
-atsinst
1
a)
b)
est sin3t
5
c)
e-at sin3t
5
d)
5
5
(s-3)2+25A
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)
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