Consider the variable coefficient linear non-homogeneous ODE where and where u and are unknown functions. O c(x) = The two linearly independent solutions of the associated homogeneous equation are O (a) Which of the following is the expression for u? O The solution method involves solving two first order ODES for u and v. 23 O 3 cosh(32)2+2 sinh(32) O A particular solution to the non-homogeneous equation can be found using the method of variation of parameters, 3 cosh(3z)z+2 sinh(32) sinh(32)z5 -3 cosh(3x)x-2 sinh(3x) O sinh(3z) 5 3 cosh(32)z+2 sinh(32) a(x) = (b) Which of the following is the expression for u? 23 3 cosh(32)x+2 sinh(3x) -3 cosh(3x)x - 2 sinh(32) 23 sinh(3z) 5 3 cosh(32)2+2 sinh(32) a(z)y" + b(z)y' + c(z)y=d(z) 18 sinh(3r)a + 18 cosh(32) 24 sinh(32) 5 -3 cosh(32)x-2 sinh(3x) z3 3 cosh(32)x+2 sinh(3x) b(x) = d(x) = 31=sinh(32), 3=2 p=1+2, (9z2 _6)sinh(3z) 24 -3 cosh(3x)x - 2 sinh(3x)
Consider the variable coefficient linear non-homogeneous ODE where and where u and are unknown functions. O c(x) = The two linearly independent solutions of the associated homogeneous equation are O (a) Which of the following is the expression for u? O The solution method involves solving two first order ODES for u and v. 23 O 3 cosh(32)2+2 sinh(32) O A particular solution to the non-homogeneous equation can be found using the method of variation of parameters, 3 cosh(3z)z+2 sinh(32) sinh(32)z5 -3 cosh(3x)x-2 sinh(3x) O sinh(3z) 5 3 cosh(32)z+2 sinh(32) a(x) = (b) Which of the following is the expression for u? 23 3 cosh(32)x+2 sinh(3x) -3 cosh(3x)x - 2 sinh(32) 23 sinh(3z) 5 3 cosh(32)2+2 sinh(32) a(z)y" + b(z)y' + c(z)y=d(z) 18 sinh(3r)a + 18 cosh(32) 24 sinh(32) 5 -3 cosh(32)x-2 sinh(3x) z3 3 cosh(32)x+2 sinh(3x) b(x) = d(x) = 31=sinh(32), 3=2 p=1+2, (9z2 _6)sinh(3z) 24 -3 cosh(3x)x - 2 sinh(3x)
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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Transcribed Image Text:Consider the variable coefficient linear non-homogeneous ODE
where
and
where u and v are unknown functions.
c(x) =
O
The two linearly independent solutions of the associated homogeneous equation are
sinh(3r) 5
3 cosh (3x)x+2 sinh(3x)
23
O 3 cosh(32)+2 sinh(3a)
(a) Which of the following is the expression for u?
O
O
The solution method involves solving two first order ODES for u and v.
z3
3 cosh(3x)x+2 sinh(3x)
sinh(32) 5
-3 cosh(3x)x-2 sinh(3x)
O
a(x) =
A particular solution to the non-homogeneous equation can be found using the method of variation of parameters,
(b) Which of the following is the expression for u?
2:3
3 cosh(3x)x+2 sinh(3x)
-3 cosh (3x)x - 2 sinh(3x)
T3
sinh(32)z5
3 cosh(3)+2 sinh(3)
a(z)y" + b(r)y' + c(x)y=d(x)
18 sinh(3x)x+18 cosh (3x)
4
sinh(32) 5
-3 cosh(3x)x-2 sinh(3x)
2:3
3 cosh(3x)x+2 sinh(3x)
"1
b(x) =
d(x) =
31 = sinh(32), My = -2
yp = 1 + 2,
(9x² - 6) sinh(3x)
-3 cosh (3x)x - 2 sinh(3x)
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