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One of the following is linearly dependent set. (A) {x², x, 1} (B) {x²,1} (C) {e*.x, 1} (D) {x².0)

One of the following is linearly dependent set. (A) {x², x, 1} (B) {x²,1} (C) {e*.x, 1} (D) {x².0)

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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differential equations please solve questionnnnnnn 6

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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