c) u' - 6u = 6 d)-1 Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are): c) 0 b) 0,-1 a) 0,1
c) u' - 6u = 6 d)-1 Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are): c) 0 b) 0,-1 a) 0,1
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
please solve question 10
![Q1) L-1
a) cosht -1
b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t)
Q2) The general solution of y"" + 2y" -y' - 2y = 0, is:
a) y(x) = c₂e²x + c₂e-* + c3e*
c) y(x) = c₁e²x + c₂ex
b) y(x) = c₂e-2x + c₂e-*
d) y(x) = c₂e-2x + ₂x + c3e-*
Q3) Evaluate L (e-2t sin4t):
4
s+2
a)
5+2
s²+8s+20
d)
s²+45+20
S²+45+20
s²+85+20
Q4) If the power series method was used to solve the following ODE..
(x-0.5)y"-5 y' + (x² - 1) y=0, x= 0. Then the interval of convergence, is:
a)
b) (-1,1)
c) (0,00)
Q5) fest dt =
е
b) 0
c)=²
d) ∞
.
y
Q6) If you know that the radius of convergent of the series method for the ODE
y"+y' + = 0, xo = 2 is 5. Find the value for b. (b < 0) :
(a) -5
x-b
(b)-3
(c)-2
d) <-8
Q7) L(y") =
=
a) s²L(y(x)) + sy(0) - y'(0)
b) s² L(y(x)) + sy(0) + y'(0)
c) s²L(y(x)) - sy(0) - y'(0)
d) s²L(y(x)) - sy(0) + y'(0)
Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant
coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is:
a) C₁ + C₂x + C3x² + e²x [Acos(x) + Bsin(x)]
b) C₁+C₂x + C3x² +e5x[Acos (2x) + Bsin(2x)]
c) C₁x + ₂x² + C3x³ + ex[Acos (5x) + Bsin(5x)]
d) C₁ + C₂x + C3x² + e²x [Acos (5x) + Bsin(5x)]
Q9) 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
Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are):
c) 0
b) 0,-1
a) 0,1
d)-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb17f493-0cbf-4721-a8d7-b4940a84a3ac%2F046bd405-645f-48b2-839f-f086b36700a4%2Fqaqe07b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1) L-1
a) cosht -1
b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t)
Q2) The general solution of y"" + 2y" -y' - 2y = 0, is:
a) y(x) = c₂e²x + c₂e-* + c3e*
c) y(x) = c₁e²x + c₂ex
b) y(x) = c₂e-2x + c₂e-*
d) y(x) = c₂e-2x + ₂x + c3e-*
Q3) Evaluate L (e-2t sin4t):
4
s+2
a)
5+2
s²+8s+20
d)
s²+45+20
S²+45+20
s²+85+20
Q4) If the power series method was used to solve the following ODE..
(x-0.5)y"-5 y' + (x² - 1) y=0, x= 0. Then the interval of convergence, is:
a)
b) (-1,1)
c) (0,00)
Q5) fest dt =
е
b) 0
c)=²
d) ∞
.
y
Q6) If you know that the radius of convergent of the series method for the ODE
y"+y' + = 0, xo = 2 is 5. Find the value for b. (b < 0) :
(a) -5
x-b
(b)-3
(c)-2
d) <-8
Q7) L(y") =
=
a) s²L(y(x)) + sy(0) - y'(0)
b) s² L(y(x)) + sy(0) + y'(0)
c) s²L(y(x)) - sy(0) - y'(0)
d) s²L(y(x)) - sy(0) + y'(0)
Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant
coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is:
a) C₁ + C₂x + C3x² + e²x [Acos(x) + Bsin(x)]
b) C₁+C₂x + C3x² +e5x[Acos (2x) + Bsin(2x)]
c) C₁x + ₂x² + C3x³ + ex[Acos (5x) + Bsin(5x)]
d) C₁ + C₂x + C3x² + e²x [Acos (5x) + Bsin(5x)]
Q9) 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
Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are):
c) 0
b) 0,-1
a) 0,1
d)-1
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