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 2. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (ln|4x +31)], transform it to z. A. 64(D² - D+)y = 16e²² sec²z C. 64(D²D+)y = 16e2z sec²2z D. (D²-4D + 4)y=e2z sec²2z B. (D² - 4D + 4)y = e²z sec²z C. Variation of Parameters None of the choices D. 3. Given: x³y" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, write the transformed equation in z. A. (D³-6D² + 11D - 12)y = 2e¹² + z B. (D³ - D² + 11D 12)y = 2e¹² + Inz C. (D³-6D² + 11D - 12)y = e²² + z D. (D³ - D² + 11D - 12)y = 2e¹² + z 4. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x² + Inx, what are the roots of the equation. A. m = 3,2 ± √√2i m = 4,1 ± √10i C. D. m = 4,1 ± √√2i B. m 1,4 ± √10i = C. 5. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, write the complementary solution in x. A. Ye= C₁x³ + x² [c₂cos√2x + c3sin√2x] Ye= C₁x¹ + x[c₂cos√10x + c3sin√10x] Yc = C₁x¹ + x[c₂cos√2x + c3sin√2x] D. B. Ye= Yc = C₁x + x¹ [c₂cos√10x + c3sin√10x]
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 2. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (ln|4x +31)], transform it to z. A. 64(D² - D+)y = 16e²² sec²z C. 64(D²D+)y = 16e2z sec²2z D. (D²-4D + 4)y=e2z sec²2z B. (D² - 4D + 4)y = e²z sec²z C. Variation of Parameters None of the choices D. 3. Given: x³y" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, write the transformed equation in z. A. (D³-6D² + 11D - 12)y = 2e¹² + z B. (D³ - D² + 11D 12)y = 2e¹² + Inz C. (D³-6D² + 11D - 12)y = e²² + z D. (D³ - D² + 11D - 12)y = 2e¹² + z 4. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x² + Inx, what are the roots of the equation. A. m = 3,2 ± √√2i m = 4,1 ± √10i C. D. m = 4,1 ± √√2i B. m 1,4 ± √10i = C. 5. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, write the complementary solution in x. A. Ye= C₁x³ + x² [c₂cos√2x + c3sin√2x] Ye= C₁x¹ + x[c₂cos√10x + c3sin√10x] Yc = C₁x¹ + x[c₂cos√2x + c3sin√2x] D. B. Ye= Yc = C₁x + x¹ [c₂cos√10x + c3sin√10x]
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 48PS
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