D. Multiple Choice1. Given: [(4x + 3)²D² − 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case isthis?A. Cauchy-Euler EquationB. Legendre EquationC.D.Variation of ParametersNone of the choices2. 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 sec²zB. (D² - 4D + 4)y = e²² sec²zC.D.64(D²D+)y = 16e²² sec²2z(D² - 4D + 4)y = e²² sec²2z3. Given: x³y" - 3x²y" + 6xy' - 12y = 2x¹ + lnx, write the transformed equation in z.A. (D³ - 6D² + 11D - 12)y = 2e¹² + zC. (D³ - 6D² + 11D - 12)y = e²z+z(D³-D² + 11D - 12)y = 2e¹² + zB.(D³ - D² + 11D - 12)y = 2e¹² + InzD.4. Given: x³y"" - 3x²y" + 6xy' - 12y = 2x¹ + Inx, what are the roots of the equation.A. m = 3,2 ± √2iC.m = 4,1 ± √10iB. m 1,4 ± √10iD.m = 4,1 ± √√2iC.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

Answered: Image /qna-images/answer/aaa2dc32-13db-4986-96ed-79e8bb6576f9.jpg

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