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Q1: If y" + y = x², then yp = (A) x² Q2: If y" + 3y' +2.25y = -10e-1.5x, then yp = (A) Ax²e-¹5x (B) Ax²e-1.5x + Bxe-1.5x C) Ax²2e-1.5x + Bxe-1.5x + Ce-1.5x (D) Ae-1.5x Q3: The Wronskian of the homogeneous solution of y" + y = cscx, is= (A)-1 (B) (C) 0 (D) 1 ,2x (A) c₁ex + c₂xe* + c3e²x + ₁е-2x (D) c₁e²x + c₂e-2x + c3sinx + C4cosx (A) m³-6m² +11m-6=0 -11m-6=0 (C) {ex.x, 1} Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex + c3e²x + c₂e-2x (C) c₁e* + c₂e4x Q5: The characteristic equation of x³y" − 3x²y" + 6xy' - 6y = 0, is: (B) m³ + 6m²-11m+6=0 Q6: One of the following is linearly dependent set. (A) {x², x, 1} Q7: The solution of y(4) = 0, is: (A) Cx³ (B) C₁ + C₂x + C3x² + C4x³ (C) C₁+C₂ex + С3e²x + Q8: The recurrence relation of the power series solution of y" + xy (n-1) an ,n=1,2,... (C) -42, n = 1,2,... (n+1)(n+2) an -an (B) (A) 22, n = 1,2,... n+2 n+2' {coswt} = 22 to find L-1 {3} = (A) ² +45 (B) x² + 2 Q9: Use L{1} = Q10: The solution of y" + xy = 0, is y = (A) a₁ + a₁x + ²x³+... (B) ao + a₁x + 6 (C) m³ - 6m² +11m + 6 = 0(D) m³-6m² (B) {x², 1, 1) 40x3 12 (C) x²-2 1-cos2t 4 +... (C) ao + a₁x- (B) x² + x + 1 4e³x (D) Cısinx + C2cosx + Cgxsinx +C,xcos + y = 0, is a₂ = 20, and a₂+2 = , n = 1,2,... (D) (1-n)an (n+1)(n+2)' (B) 2 (1-cost) (C): 9 (D) 2x² Aox³ 12 S Q11: Use cos2x = 2cos²x - 1and L{1}=and L{coswx} = 2+2 to find L{cos² (4x)} = (A) = (-²3-5²464) (B) (+) (C) (-²) Q12: If y"= 1, then yp= (A) x² (D) {x², 1/1,0} 1+cos ****** ·+... (D) a₁ + a₁xx³+... (D) 2 (1+cos3t) (D) ²/2 (²= + 5/2²/²4/64) (D) x + 1

Q1: If y" + y = x², then yp = (A) x² Q2: If y" + 3y' +2.25y = -10e-1.5x, then yp = (A) Ax²e-¹5x (B) Ax²e-1.5x + Bxe-1.5x C) Ax²2e-1.5x + Bxe-1.5x + Ce-1.5x (D) Ae-1.5x Q3: The Wronskian of the homogeneous solution of y" + y = cscx, is= (A)-1 (B) (C) 0 (D) 1 ,2x (A) c₁ex + c₂xe* + c3e²x + ₁е-2x (D) c₁e²x + c₂e-2x + c3sinx + C4cosx (A) m³-6m² +11m-6=0 -11m-6=0 (C) {ex.x, 1} Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex + c3e²x + c₂e-2x (C) c₁e* + c₂e4x Q5: The characteristic equation of x³y" − 3x²y" + 6xy' - 6y = 0, is: (B) m³ + 6m²-11m+6=0 Q6: One of the following is linearly dependent set. (A) {x², x, 1} Q7: The solution of y(4) = 0, is: (A) Cx³ (B) C₁ + C₂x + C3x² + C4x³ (C) C₁+C₂ex + С3e²x + Q8: The recurrence relation of the power series solution of y" + xy (n-1) an ,n=1,2,... (C) -42, n = 1,2,... (n+1)(n+2) an -an (B) (A) 22, n = 1,2,... n+2 n+2' {coswt} = 22 to find L-1 {3} = (A) ² +45 (B) x² + 2 Q9: Use L{1} = Q10: The solution of y" + xy = 0, is y = (A) a₁ + a₁x + ²x³+... (B) ao + a₁x + 6 (C) m³ - 6m² +11m + 6 = 0(D) m³-6m² (B) {x², 1, 1) 40x3 12 (C) x²-2 1-cos2t 4 +... (C) ao + a₁x- (B) x² + x + 1 4e³x (D) Cısinx + C2cosx + Cgxsinx +C,xcos + y = 0, is a₂ = 20, and a₂+2 = , n = 1,2,... (D) (1-n)an (n+1)(n+2)' (B) 2 (1-cost) (C): 9 (D) 2x² Aox³ 12 S Q11: Use cos2x = 2cos²x - 1and L{1}=and L{coswx} = 2+2 to find L{cos² (4x)} = (A) = (-²3-5²464) (B) (+) (C) (-²) Q12: If y"= 1, then yp= (A) x² (D) {x², 1/1,0} 1+cos ****** ·+... (D) a₁ + a₁xx³+... (D) 2 (1+cos3t) (D) ²/2 (²= + 5/2²/²4/64) (D) x + 1

Advanced Engineering Mathematics
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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Q1: If y" + y = x², then yp = (A) x² Q2: If y" + 3y' +2.25y = -10e-1.5x, then yp = (A) Ax²e-15x (B) Ax²e-1.5x + Bxe-1.5x C) Ax²e-1.5x + Bxe-1.5x + Ce-1.5x (D) Ae-1.5x Q3: The Wronskian of the homogeneous solution of y" + y = cscx, is= (A)-1 Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex + c3e²x + ₁е-2x (C) c₁e* + c₂e4x Q5: The characteristic equation of x³y" - 3x²y" + 6xy' - 6y = 0, is: (B) m³ + 6m² -11m+6=0 Q6: One of the following is linearly dependent set. (A) {x², x, 1} Q7: The solution of y(4) = 0, is: (A) Cx³ (B) C₁ + C₂x + C3x² + 4x³ (C) C₁+C₂ex + С3e²x + ₁e³x n+2' n = 1,2,... S Q9: Use L{1}={coswt} = 52+2 to find L-1, Q10: The solution of y" + xy = 0, is y = (B) ao + a₁x + aox³ 6 (A) ao + a₁x + ·+... Q8: The recurrence relation of the power series solution of y" + xy + y = 0, is a₂ = 20, and a₂+2 = (A). (B) (n-1) an (n+1)(n+2) n = 1,2,... (C)2, n = 1,2,... (D) n = 1,2,... (B) x² + 2 (C) m³ - 6m² + 11m + 6 = 0(D) m³-6m² -11m-6=0 (B) {x², 1,1} (C) (ex.x, 1} aox³ 12 Q11: Use cos2x = 2cos²x - 1and L{1}=and (A) = (²-²-5² +64) (B) / (+52 +64) Q12: If y"= 1, then yp = (A) x² 1 ¹ { ₁ ³ + 45 -} = (A) +4s +... (C) x²-2 1-cos2t 4 (C) 0 (D) 1 (A) ce* +Czxe* +c3e2x +ce-2x (D) c₁e²x + c₂e-2x + c3sinx + C4cosx (A) m³ - 6m² + 11m-6=0 (B) x² + x + 1 (D) Cısinx + C2cosx +Cgxsinx +Caxco: (1-n)an (n+1)(n+2)' (D) 2x² (B) 2 (1-cost) (C) 9 (C) ao + a₁x-- S L{coswx} = 52+2 to find L{cos² (4x)} = (C) =/= ( 3 - 5 ² ²64) 40x3 12 (D) {x², 112,0} (C)=x² 1+cos 4 (D) 2 (1+cos3t) (D) ao + a₁x. aox³ 6 (D) ²/2 ( = +52 4/64) +... (D) x + 1
Transcribed Image Text:Q1: If y" + y = x², then yp = (A) x² Q2: If y" + 3y' +2.25y = -10e-1.5x, then yp = (A) Ax²e-15x (B) Ax²e-1.5x + Bxe-1.5x C) Ax²e-1.5x + Bxe-1.5x + Ce-1.5x (D) Ae-1.5x Q3: The Wronskian of the homogeneous solution of y" + y = cscx, is= (A)-1 Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex + c3e²x + ₁е-2x (C) c₁e* + c₂e4x Q5: The characteristic equation of x³y" - 3x²y" + 6xy' - 6y = 0, is: (B) m³ + 6m² -11m+6=0 Q6: One of the following is linearly dependent set. (A) {x², x, 1} Q7: The solution of y(4) = 0, is: (A) Cx³ (B) C₁ + C₂x + C3x² + 4x³ (C) C₁+C₂ex + С3e²x + ₁e³x n+2' n = 1,2,... S Q9: Use L{1}={coswt} = 52+2 to find L-1, Q10: The solution of y" + xy = 0, is y = (B) ao + a₁x + aox³ 6 (A) ao + a₁x + ·+... Q8: The recurrence relation of the power series solution of y" + xy + y = 0, is a₂ = 20, and a₂+2 = (A). (B) (n-1) an (n+1)(n+2) n = 1,2,... (C)2, n = 1,2,... (D) n = 1,2,... (B) x² + 2 (C) m³ - 6m² + 11m + 6 = 0(D) m³-6m² -11m-6=0 (B) {x², 1,1} (C) (ex.x, 1} aox³ 12 Q11: Use cos2x = 2cos²x - 1and L{1}=and (A) = (²-²-5² +64) (B) / (+52 +64) Q12: If y"= 1, then yp = (A) x² 1 ¹ { ₁ ³ + 45 -} = (A) +4s +... (C) x²-2 1-cos2t 4 (C) 0 (D) 1 (A) ce* +Czxe* +c3e2x +ce-2x (D) c₁e²x + c₂e-2x + c3sinx + C4cosx (A) m³ - 6m² + 11m-6=0 (B) x² + x + 1 (D) Cısinx + C2cosx +Cgxsinx +Caxco: (1-n)an (n+1)(n+2)' (D) 2x² (B) 2 (1-cost) (C) 9 (C) ao + a₁x-- S L{coswx} = 52+2 to find L{cos² (4x)} = (C) =/= ( 3 - 5 ² ²64) 40x3 12 (D) {x², 112,0} (C)=x² 1+cos 4 (D) 2 (1+cos3t) (D) ao + a₁x. aox³ 6 (D) ²/2 ( = +52 4/64) +... (D) x + 1
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