c) y(x) = ₂x² + ₂x-3 d) y(x) = x + ₂x³ Q20) The form of a particular solution of a) yp (t) = A sin(2t) (t)- Acos(?t) + B sin(2t) y" - 4y' - 12y = sin(2t), is: . b) yp (t) = A cos(t) d) y(t) = A cos(t) + B sin(t) x3 and h(x)
c) y(x) = ₂x² + ₂x-3 d) y(x) = x + ₂x³ Q20) The form of a particular solution of a) yp (t) = A sin(2t) (t)- Acos(?t) + B sin(2t) y" - 4y' - 12y = sin(2t), is: . b) yp (t) = A cos(t) d) y(t) = A cos(t) + B sin(t) x3 and h(x)
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 20
![.Q11) The general solution of y" - 4y' +9y = 0, is:
a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t)
c)y(t) = c₂e2t cos(√5 t) + c₂e²t sin (√5 t)
b)y(t) = cet cos(√5 t) + c₂e²sin (√5t)
d) y(t) = ce cos(5 t) + c₂esin (5 t)
012) The formula of the particular solution yp of y(4) + 4y" = 3 sin(2t) - 5cos2t, is:
a) yp= Asin(t) + Bcos(t)
c) yp
Asin(2t) + Bcos(2t)
b) yp = Atsin(t) + Btcos(t)
d) yp = Atsin(2t) + Btcos (2t)]
Q13) The general solution for y' = 6y²x, is:
a) = 3x² + c
b)
= x² + c
c) == 3x² + c d) == x² + c
Q14) The solution of y" + y'= 0 by using power series method, is:
a) y(x) = ao + a₁(1)
c) y(x) = ao + a₁(x-
x²x²x²
21 31
x²x²
..)
x²
b) y(x) = ao + a₂ (1+ 21
d)y(x) = ao + a₂(x+:
Q15) Given that y₁ (t) = t¹ is solution for 2t²y" + ty' - 3y = 0,t> 0, then y₂ (t) is:
41 51
x5
x¹
314151)
x²
=+=
a) t
b) tz
Q16) L-¹ (5-3)²+25)
d) ti
c) tz
etsinst
5
=
a)
e-3t sin3t
eatsinst
b)
est sin3t
5
C)
d)
Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t):
a)
(s+2)²+16
25² +18
b) (5-2)2+16
c)
2s²+18
(5+2)2+16
25+18
(S-2)2+16
25² +18
Q18) Combine the following power series expressions into a single power series.
En 1(n+1)(x-2)n-1 + Σon(x - 2)"
a) Eno(2n + 1)(x)"
b) En-o(2n + 2)(x)"
c) Eno(2n + 2)(x - 2)"
d)
(2n + 1)(x-2)"
Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is:
a) y(x) = C₁x² + ₂x³
b) y(x) = C₁x + ₂x-3
c) y(x) = ₂x² + ₂x-3
d) y(x) = x² + ₂x³
Q20) The form of a particular solution of
y"-4y' - 12y = sin(2t), is:
a) yp (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)
Q21) One of the following is correct for functions the f(x) = 1, g(x) = x³ and h(x) = ln(x):
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 independe
d) W (f(x), g(x), h(x)) = 9
=
is:
(3s+2)(S-2)
S'
Q22) The inverse Laplace transform of H(s)
b) f(t)= e+e-
a) f(t) ==e¹+¹e²t
-3 -2
8
-2,
c) f(t) = ¹ + 1 e
e-2t
d)f (t) ==³e²¹ +²e²t
Q23) The kernel of the Laplace transform of f(t), t > 0, is:
b) e-t
c) e-st
d) e-s
a) e
Q24) The Integrating factor which make (3x2y + 2xy + y³) dx + (x² + y²)dy = 0 exact, is:
a) e-3x
b) ex
d) e 3x
b) -2sinhnt
c)-2cosnt
d) -2sinnt
Q25) L-1
-2s
S²+T²
a) -2coshnt
=
·+...)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5cd78a4-f27a-424f-b074-c88bc5dd4dc9%2Fd0e5dbce-74fd-49a0-9483-b5501b7a6b75%2Fmwm2jvk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:.Q11) The general solution of y" - 4y' +9y = 0, is:
a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t)
c)y(t) = c₂e2t cos(√5 t) + c₂e²t sin (√5 t)
b)y(t) = cet cos(√5 t) + c₂e²sin (√5t)
d) y(t) = ce cos(5 t) + c₂esin (5 t)
012) The formula of the particular solution yp of y(4) + 4y" = 3 sin(2t) - 5cos2t, is:
a) yp= Asin(t) + Bcos(t)
c) yp
Asin(2t) + Bcos(2t)
b) yp = Atsin(t) + Btcos(t)
d) yp = Atsin(2t) + Btcos (2t)]
Q13) The general solution for y' = 6y²x, is:
a) = 3x² + c
b)
= x² + c
c) == 3x² + c d) == x² + c
Q14) The solution of y" + y'= 0 by using power series method, is:
a) y(x) = ao + a₁(1)
c) y(x) = ao + a₁(x-
x²x²x²
21 31
x²x²
..)
x²
b) y(x) = ao + a₂ (1+ 21
d)y(x) = ao + a₂(x+:
Q15) Given that y₁ (t) = t¹ is solution for 2t²y" + ty' - 3y = 0,t> 0, then y₂ (t) is:
41 51
x5
x¹
314151)
x²
=+=
a) t
b) tz
Q16) L-¹ (5-3)²+25)
d) ti
c) tz
etsinst
5
=
a)
e-3t sin3t
eatsinst
b)
est sin3t
5
C)
d)
Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t):
a)
(s+2)²+16
25² +18
b) (5-2)2+16
c)
2s²+18
(5+2)2+16
25+18
(S-2)2+16
25² +18
Q18) Combine the following power series expressions into a single power series.
En 1(n+1)(x-2)n-1 + Σon(x - 2)"
a) Eno(2n + 1)(x)"
b) En-o(2n + 2)(x)"
c) Eno(2n + 2)(x - 2)"
d)
(2n + 1)(x-2)"
Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is:
a) y(x) = C₁x² + ₂x³
b) y(x) = C₁x + ₂x-3
c) y(x) = ₂x² + ₂x-3
d) y(x) = x² + ₂x³
Q20) The form of a particular solution of
y"-4y' - 12y = sin(2t), is:
a) yp (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)
Q21) One of the following is correct for functions the f(x) = 1, g(x) = x³ and h(x) = ln(x):
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 independe
d) W (f(x), g(x), h(x)) = 9
=
is:
(3s+2)(S-2)
S'
Q22) The inverse Laplace transform of H(s)
b) f(t)= e+e-
a) f(t) ==e¹+¹e²t
-3 -2
8
-2,
c) f(t) = ¹ + 1 e
e-2t
d)f (t) ==³e²¹ +²e²t
Q23) The kernel of the Laplace transform of f(t), t > 0, is:
b) e-t
c) e-st
d) e-s
a) e
Q24) The Integrating factor which make (3x2y + 2xy + y³) dx + (x² + y²)dy = 0 exact, is:
a) e-3x
b) ex
d) e 3x
b) -2sinhnt
c)-2cosnt
d) -2sinnt
Q25) L-1
-2s
S²+T²
a) -2coshnt
=
·+...)
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