1. Given:[(4x + 3)²D? – 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. Variation of Parameters D. None of the choices 2. Given:[(4x + 3)²D – 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec²(ln|4x + 3|)], transform it to z. A. 64(D² – D+)y = 16e2²sec²z B. (D² – 4D + 4)y = e2²sec²z C. 64(D² – D+)y = 16e2²sec²2z D. (D² – 4D + 4)y = e2² sec²2z 3. Given: x³y"" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z. C. (D³ – 6D² + 11D – 12)y = e2z + z (D³ – D² + 11D – 12)y = 2e4z +z %3D A. (D3 – 6D² + 11D – 12)y = 2e4z +z (D³ – D² + 11D – 12)y = 2e4z + Inz D.
1. Given:[(4x + 3)²D? – 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. Variation of Parameters D. None of the choices 2. Given:[(4x + 3)²D – 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec²(ln|4x + 3|)], transform it to z. A. 64(D² – D+)y = 16e2²sec²z B. (D² – 4D + 4)y = e2²sec²z C. 64(D² – D+)y = 16e2²sec²2z D. (D² – 4D + 4)y = e2² sec²2z 3. Given: x³y"" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z. C. (D³ – 6D² + 11D – 12)y = e2z + z (D³ – D² + 11D – 12)y = 2e4z +z %3D A. (D3 – 6D² + 11D – 12)y = 2e4z +z (D³ – D² + 11D – 12)y = 2e4z + Inz D.
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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![1. Given:[(4x + 3)²D? – 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
С.
Variation of Parameters
D.
None of the choices
2. Given:[(4x + 3)²D? – 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], transform it to z.
A. 64(D² – D+)y = 16e2²sec²z
B. (D² – 4D + 4)y = e2²sec²z
64(D² – D+)y = 16e2² sec²2z
D. (D² – 4D + 4)y = e2² sec²2z
C.
3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z.
C.
(D3 – 6D² + 11D – 12)y = 2e4z + z
(D³ – D² + 11D – 12)y = 2e4z + Inz
(D3 – 6D² + 11D – 12)y = e2z + z
D.
(D³ – D² + 11D – 12)y = 2e*z + z
4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation.
A. m = 3,2 ± vZi
В. т%3D 1,4 V10i
С.
m = 4,1 ± V10i
D.
m = 4,1 ± /2i
5. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x.
Ye = C,x³ + x²[c2cosv2x + c3sinv2x]
B. y. = c1x + x*[c2cosv10x + c3sinv10x]
Ye = C1x* + x[c2cos/10x + c3sinv10x]
D. Yc = C1x* + x[c2cosv2x + c3sinv2x]
А.
С.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6b903ef-f3cc-4cd7-854f-fe650f5bd182%2Fecd16c5b-5af5-4ea1-8649-33da4631f62b%2Fauwmt9b_processed.png&w=3840&q=75)
Transcribed Image Text:1. Given:[(4x + 3)²D? – 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
С.
Variation of Parameters
D.
None of the choices
2. Given:[(4x + 3)²D? – 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], transform it to z.
A. 64(D² – D+)y = 16e2²sec²z
B. (D² – 4D + 4)y = e2²sec²z
64(D² – D+)y = 16e2² sec²2z
D. (D² – 4D + 4)y = e2² sec²2z
C.
3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z.
C.
(D3 – 6D² + 11D – 12)y = 2e4z + z
(D³ – D² + 11D – 12)y = 2e4z + Inz
(D3 – 6D² + 11D – 12)y = e2z + z
D.
(D³ – D² + 11D – 12)y = 2e*z + z
4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation.
A. m = 3,2 ± vZi
В. т%3D 1,4 V10i
С.
m = 4,1 ± V10i
D.
m = 4,1 ± /2i
5. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x.
Ye = C,x³ + x²[c2cosv2x + c3sinv2x]
B. y. = c1x + x*[c2cosv10x + c3sinv10x]
Ye = C1x* + x[c2cos/10x + c3sinv10x]
D. Yc = C1x* + x[c2cosv2x + c3sinv2x]
А.
С.
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