1. Given: [(4x + 3)²D² - 12(4x + 3)Dx+64]y = 16[(4x + 3)² sec² (In 4x +31)], what special case is this? A. Cauchy-Euler Equation Legendre Equation C. Variation of Parameters D. None of the choices 2. Given: [(4x + 3)²D² - 12(4x+3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], transform it to z. A. 64(D²D+)y = 16e²sec²z C. 64(D²D+)y = 16e²sec ²2z (D² - 4D+4)y = e²² sec²2z B. (D²-4D + 4)y = e²² sec²z D. 3. Given: x³y" - 3x2y" + 6xy' - 12y = 2x + Inx, write the transformed equation in z. A. (D³-6D² +11D-12)y= 2e +2 B. (D³-D² +11D-12)y= 2e + Inz C. D. (D³-6D2 +11D-12)y=e² +2 (D²D² +11D-12)y = 2e + z
1. Given: [(4x + 3)²D² - 12(4x + 3)Dx+64]y = 16[(4x + 3)² sec² (In 4x +31)], what special case is this? A. Cauchy-Euler Equation Legendre Equation C. Variation of Parameters D. None of the choices 2. Given: [(4x + 3)²D² - 12(4x+3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], transform it to z. A. 64(D²D+)y = 16e²sec²z C. 64(D²D+)y = 16e²sec ²2z (D² - 4D+4)y = e²² sec²2z B. (D²-4D + 4)y = e²² sec²z D. 3. Given: x³y" - 3x2y" + 6xy' - 12y = 2x + Inx, write the transformed equation in z. A. (D³-6D² +11D-12)y= 2e +2 B. (D³-D² +11D-12)y= 2e + Inz C. D. (D³-6D2 +11D-12)y=e² +2 (D²D² +11D-12)y = 2e + z
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
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![1. Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], 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)D +64]y = 16[(4x + 3)² sec² (in 4x +31)], transform it to z.
A. 64(D²D+)y = 16e²z sec²z
C.
64(D²D+)y = 16e²² sec²2z
(D² - 4D + 4)y = e²² sec²2z
B.
(D²4D+4)y= ²² sec²z
D.
3. Given: x³y"" - 3x2y" + 6xy' - 12y = 2x* + Inx, write the transformed equation in z.
A. (D³-6D² + 11D-12)y=2e¹² + z
(D³-6D² + 11D-12)y=e² + z
(D³D² + 11D - 12)y=2e4z + z
B. (D³-D² + 11D-12)y = 2e4² + Inz
C.
D.
4. Given: x³y""-3x2y" + 6xy' - 12y = 2x* + Inx, what are the roots of the equation.
A. m = 3,2 ± √2i
m = 4,1 ± √10i
C.
B. m = = 1,4 ± √10i
D.
m = 4,1± √2i
5. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x+ + Inx, write the complementary solution in x.
Ye= C₁x³ + x² [c₂cos√2x + casin√2x]
B. Y = C₁x + x[c₂cos√10x + casin√10x] D.
Ye= C₁x + x[c₂cos√10x + c3sin√10x]
c =
Ye=₁x + x[c₂cos√2x + c₂sin√2x]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe632c28a-3285-4607-b401-8e192bee1a29%2F2657a37c-bf66-41e1-886c-883a63ff206b%2Fr6j38vj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], 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)D +64]y = 16[(4x + 3)² sec² (in 4x +31)], transform it to z.
A. 64(D²D+)y = 16e²z sec²z
C.
64(D²D+)y = 16e²² sec²2z
(D² - 4D + 4)y = e²² sec²2z
B.
(D²4D+4)y= ²² sec²z
D.
3. Given: x³y"" - 3x2y" + 6xy' - 12y = 2x* + Inx, write the transformed equation in z.
A. (D³-6D² + 11D-12)y=2e¹² + z
(D³-6D² + 11D-12)y=e² + z
(D³D² + 11D - 12)y=2e4z + z
B. (D³-D² + 11D-12)y = 2e4² + Inz
C.
D.
4. Given: x³y""-3x2y" + 6xy' - 12y = 2x* + Inx, what are the roots of the equation.
A. m = 3,2 ± √2i
m = 4,1 ± √10i
C.
B. m = = 1,4 ± √10i
D.
m = 4,1± √2i
5. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x+ + Inx, write the complementary solution in x.
Ye= C₁x³ + x² [c₂cos√2x + casin√2x]
B. Y = C₁x + x[c₂cos√10x + casin√10x] D.
Ye= C₁x + x[c₂cos√10x + c3sin√10x]
c =
Ye=₁x + x[c₂cos√2x + c₂sin√2x]
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