a) y(t)=ce²t cos(5 t) + c₂e² sin c)y(t)=ce²t cos(√5 t) + c₂et sin (√5 t) Q8) The inverse Laplace transform of H(s) d) y(t) = ce cos(5 t) + c 1 is: F T (35+2)(5-2) 2t a) f(t)=e+ b) f(t) ==e+ 8 1-2t +²e²t d)f(t)= c) f(t) ==e+e om The solution of y" + y'= 0 by using power series method, is: -2t h) y(x) = a + a₂ (1
a) y(t)=ce²t cos(5 t) + c₂e² sin c)y(t)=ce²t cos(√5 t) + c₂et sin (√5 t) Q8) The inverse Laplace transform of H(s) d) y(t) = ce cos(5 t) + c 1 is: F T (35+2)(5-2) 2t a) f(t)=e+ b) f(t) ==e+ 8 1-2t +²e²t d)f(t)= c) f(t) ==e+e om The solution of y" + y'= 0 by using power series method, is: -2t h) y(x) = a + a₂ (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
SOLVE Q8
Transcribed Image Text:Q1) One of the following is correct for functions the f(x) = 1, g(x)= x³ and h(x)
M
a) f(x), g(x) and h(x) are linearly dependent
c) W (f(x), g(x), h(x)) = 0
b) f(x), g(x) and h(x) are linearly independent
d) W(f(x), g(x), h(x)) = 9
Q2) L-1
-2s
2+3
H
a) -2coshnt
b)-2sinhnt
c)-2cosnt
d)-2sinnt
Q3) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, is:
a) e-3x
b) ei*
d) e³x
Q4) 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
Q5) The general solution of 2x2y" + 3xy'-15y = 0, is:
a) y(x) = ₂x² + ₂x³
b) y(x) = ₂x + ₂x-3
c) y(x) = c₁x² + ₂x-3
d) y(x) = c₁x + ₂x³
Q6) Evaluate L (2 e-2 sin4t -0.5 cos3t):
8
S
a)
(s+2)² +16
b)
c) (8+2)² +16 23²418
(5-2)2+16
25² +18
2s² +18
(s-2)² +16
Q7) The general solution of y"-4y' +9y = 0, is:
a) y(t)=ce²t cos(5 t) + c₂e²tsin (5 t)
c)y(t) = cet cos(√5 t) + c₂e²t sin (√5 t)
Q8) The inverse Laplace transform of H(s):
b)y(t) = ce cos(√5 t) + c₂e¹sin (√5t)
d) y(t) = ce cos(5 t) + cesin (5 t)
1
=
is:
.
(35+2)(5-2)
a) f(t) ==e+e²t
b) f(t) ==e.
8
c) f(t) ==e+e-2t
d)f(t) ==e.
+²e²t
Q9) The solution of y" + y'= 0 by using power series method, is:
a) y(x) = ao + a₁ (1-
11
b) y(x) = a + a₁(1+
21
31
41
St
21
c) y(x) = a₁ + a₁(x-+
d)y(x) = a + a₂(x + ==
51
-
e-2t
1
2s² +18
+ +
ii
41
41
51
++
+ ...)
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