D. Multiple Choice 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is this? A. B. Legendre Equation Cauchy-Euler Equation C. D. A. B. 2. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x +31)], transform it to z. A. 64(D² - D+)y = 16e²² sec²z C. 64(D²D+)y = 16e²z sec²2z (D² - 4D + 4)y = e2² sec²2z B. (D² - 4D + 4)y = e²² sec²z D. Variation of Parameters None of the choices 3. Given: x³y" - 3x2y" + 6xy' - 12y = 2x¹ + lnx, write the transformed equation in z. (D³6D² + 11D - 12)y = 2e¹² + z (D³-6D² + 11D - 12)y = e²² + z (D³ - D² + 11D 12)y = 2e¹² + z (D³ - D² + 11D - 12)y = 2e¹² + Inz C. D. 9
D. Multiple Choice 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is this? A. B. Legendre Equation Cauchy-Euler Equation C. D. A. B. 2. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x +31)], transform it to z. A. 64(D² - D+)y = 16e²² sec²z C. 64(D²D+)y = 16e²z sec²2z (D² - 4D + 4)y = e2² sec²2z B. (D² - 4D + 4)y = e²² sec²z D. Variation of Parameters None of the choices 3. Given: x³y" - 3x2y" + 6xy' - 12y = 2x¹ + lnx, write the transformed equation in z. (D³6D² + 11D - 12)y = 2e¹² + z (D³-6D² + 11D - 12)y = e²² + z (D³ - D² + 11D 12)y = 2e¹² + z (D³ - D² + 11D - 12)y = 2e¹² + Inz C. D. 9
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
![D. Multiple Choice
1. Given: [(4x + 3)²D² − 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is
this?
A. Cauchy-Euler Equation
B. Legendre Equation
C.
D.
Variation of Parameters
None of the choices
2. Given: [(4x + 3)²D² − 12 (4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (ln|4x + 3)], transform it to z.
A. 64(D²D+)y = 16e22 sec²z
B. (D² - 4D + 4)y = e²² sec²z
C.
D.
64(D²D+)y = 16e²² sec²2z
(D² - 4D + 4)y = e²² sec²2z
3. Given: x³y" - 3x²y" + 6xy' - 12y = 2x¹ + lnx, write the transformed equation in z.
A. (D³ - 6D² + 11D - 12)y = 2e¹² + z
C. (D³ - 6D² + 11D - 12)y = e²z+z
(D³-D² + 11D - 12)y = 2e¹² + z
B.
(D³ - D² + 11D - 12)y = 2e¹² + Inz
D.
4. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, what are the roots of the equation.
A. m = 3,2 ± √2i
C.
m = 4,1 ± √10i
B. m 1,4 ± √10i
D.
m = 4,1 ± √√2i
C.
5. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + lnx, write the complementary solution in x.
A. Y₁ = ₁x³ + x² [c₂cos√2x + c3sin√2x] Yc = C₁x¹ + x[c₂cos√10x + c3sin√10x]
Yc = C₁x¹ + x[c₂cos√2x + c3sin√2x]
B. Yc = C₁x + x¹ [c₂cos√10x + c3sin√10x]
D.
99](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb8d5b1d-1288-414c-b30c-65d320db1a85%2Faaa2dc32-13db-4986-96ed-79e8bb6576f9%2F0zqjy6s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:D. Multiple Choice
1. Given: [(4x + 3)²D² − 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is
this?
A. Cauchy-Euler Equation
B. Legendre Equation
C.
D.
Variation of Parameters
None of the choices
2. Given: [(4x + 3)²D² − 12 (4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (ln|4x + 3)], transform it to z.
A. 64(D²D+)y = 16e22 sec²z
B. (D² - 4D + 4)y = e²² sec²z
C.
D.
64(D²D+)y = 16e²² sec²2z
(D² - 4D + 4)y = e²² sec²2z
3. Given: x³y" - 3x²y" + 6xy' - 12y = 2x¹ + lnx, write the transformed equation in z.
A. (D³ - 6D² + 11D - 12)y = 2e¹² + z
C. (D³ - 6D² + 11D - 12)y = e²z+z
(D³-D² + 11D - 12)y = 2e¹² + z
B.
(D³ - D² + 11D - 12)y = 2e¹² + Inz
D.
4. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, what are the roots of the equation.
A. m = 3,2 ± √2i
C.
m = 4,1 ± √10i
B. m 1,4 ± √10i
D.
m = 4,1 ± √√2i
C.
5. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + lnx, write the complementary solution in x.
A. Y₁ = ₁x³ + x² [c₂cos√2x + c3sin√2x] Yc = C₁x¹ + x[c₂cos√10x + c3sin√10x]
Yc = C₁x¹ + x[c₂cos√2x + c3sin√2x]
B. Yc = C₁x + x¹ [c₂cos√10x + c3sin√10x]
D.
99
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