1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 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)²Dž – 12(4x + 3)D, + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], transform it to z. A. 64(D? – D+)y = 16e2" sec²z B. (D² – 4D + 4)y = e2# sec²z C. 64(D² – D+)y = 16e2 sec²2z D. (D² – 4D + 4)y = e2# sec²2z 3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z. A. (D3 – 6D2 + 11D – 12)y = 2e4% + z B. (D³ – D² + 11D – 12)y = 2e*z + Inz C. (D3 – 6D2 + 11D – 12)y = e2z + z D. (D³ – D? + 11D – 12)y = 2e** +z %3D 4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation. A. m = 3,2 + v2i B. m = 1,4 ± V10i C. m = 4,1 ± V10i D. m = 4,1 t /2i 5. Given: x*y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x. C. y. = C,x* + x[c2cosv10x + c3sin/10x] Ye = C1x* + x[c2cosv2x + c3sinv2x] Ye = C,x³ + x?[c2cosv2x + c3sinv2x] B. Ye = c,x + x*[c2cosv10x + c3sinv10x] A.
1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 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)²Dž – 12(4x + 3)D, + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], transform it to z. A. 64(D? – D+)y = 16e2" sec²z B. (D² – 4D + 4)y = e2# sec²z C. 64(D² – D+)y = 16e2 sec²2z D. (D² – 4D + 4)y = e2# sec²2z 3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z. A. (D3 – 6D2 + 11D – 12)y = 2e4% + z B. (D³ – D² + 11D – 12)y = 2e*z + Inz C. (D3 – 6D2 + 11D – 12)y = e2z + z D. (D³ – D? + 11D – 12)y = 2e** +z %3D 4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation. A. m = 3,2 + v2i B. m = 1,4 ± V10i C. m = 4,1 ± V10i D. m = 4,1 t /2i 5. Given: x*y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x. C. y. = C,x* + x[c2cosv10x + c3sin/10x] Ye = C1x* + x[c2cosv2x + c3sinv2x] Ye = C,x³ + x?[c2cosv2x + c3sinv2x] B. Ye = c,x + x*[c2cosv10x + c3sinv10x] A.
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
Write the letter of the correct answer and show the solutions.
![1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 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)D, + 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 = e2# sec²z
C. 64(D² – D+)y = 16e2# sec²2z
D. (D? – 4D + 4)y = e2# sec²2z
3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z.
A. (D3 – 6D² + 11D – 12)y = 2e4z + z
B. (D³ – D² + 11D – 12)y = 2e*z + Inz
C. (D³ – 6D² + 11D – 12)y = e2z + z
D. (D³ – D² + 11D – 12)y = 2e** + z
%3D
4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation.
A. m = 3,2 + v2i
B. m = 1,4 ± V10i
C. m = 4,1 ± V10i
D. m = 4,1 t /2i
5. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x.
Ye = C;x³ + x²[c2cosv2x + c3sin/2x]
B. Ye = c,x + x*[c2cosv10x + c3sinv10x]
A.
C. y. = C,x* + x[c2cosv10x + c3sin/10x]
D.
Ye = C1x* + x[c2cosv2x + c3sinvZx]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80c94c49-48ab-45bc-a9a2-ef8f8e7a1f92%2F8c13f20c-fc8f-4cd1-90c3-d7b826e9260d%2Fvihyptc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 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)D, + 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 = e2# sec²z
C. 64(D² – D+)y = 16e2# sec²2z
D. (D? – 4D + 4)y = e2# sec²2z
3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z.
A. (D3 – 6D² + 11D – 12)y = 2e4z + z
B. (D³ – D² + 11D – 12)y = 2e*z + Inz
C. (D³ – 6D² + 11D – 12)y = e2z + z
D. (D³ – D² + 11D – 12)y = 2e** + z
%3D
4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation.
A. m = 3,2 + v2i
B. m = 1,4 ± V10i
C. m = 4,1 ± V10i
D. m = 4,1 t /2i
5. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x.
Ye = C;x³ + x²[c2cosv2x + c3sin/2x]
B. Ye = c,x + x*[c2cosv10x + c3sinv10x]
A.
C. y. = C,x* + x[c2cosv10x + c3sin/10x]
D.
Ye = C1x* + x[c2cosv2x + c3sinvZx]
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