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30. Find a linear differential operator (of lowest order) that annihilates the given function: f(x) = x³ + x³ cos x - 3x sin 3x (A) Dª(D² + 1)³(D² +9)² (B) D¹(D²+1)¹(D² + 9)² (C) D¹(D² - 1)³(D² +9)² (D) D¹(D²+1)³(D² - 9)²

30. Find a linear differential operator (of lowest order) that annihilates the given function: f(x) = x³ + x³ cos x - 3x sin 3x (A) Dª(D² + 1)³(D² +9)² (B) D¹(D²+1)¹(D² + 9)² (C) D¹(D² - 1)³(D² +9)² (D) D¹(D²+1)³(D² - 9)²

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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30. Find a linear differential operator (of lowest order) that annihilates the given function: f(x) = x³ + x³ cos x - 3x sin 3x (A) D¹(D² +1)³(D² +9)² (B) D¹(D²+1)4(D² + 9)² 31. Evaluate W(1-x, x, x²) (A) 2 (B) 2x (A) m = 0,-1,1 (B) m = 0,1 (multiplicity 2) (C) D¹(D² - 1)³ (D² +9)² (D) D¹(D²+1)³(D² - 9)² 32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the DE y" + 2y" - y' = 10 are (C) -2.x (D) -2 (A) Yc=c₁e + C₂€¯² + c3 (B) Yc = C₁e + C₂xE² + c3 (C) m = 0,-1 (multiplicity 2) (D) m = 1,-1 (multiplicity 2) 33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is (C) Y₁ = ₁₂e + c₂e² + c3 (D) Ye=c₁e + c₂xе¯² + c3
Transcribed Image Text:30. Find a linear differential operator (of lowest order) that annihilates the given function: f(x) = x³ + x³ cos x - 3x sin 3x (A) D¹(D² +1)³(D² +9)² (B) D¹(D²+1)4(D² + 9)² 31. Evaluate W(1-x, x, x²) (A) 2 (B) 2x (A) m = 0,-1,1 (B) m = 0,1 (multiplicity 2) (C) D¹(D² - 1)³ (D² +9)² (D) D¹(D²+1)³(D² - 9)² 32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the DE y" + 2y" - y' = 10 are (C) -2.x (D) -2 (A) Yc=c₁e + C₂€¯² + c3 (B) Yc = C₁e + C₂xE² + c3 (C) m = 0,-1 (multiplicity 2) (D) m = 1,-1 (multiplicity 2) 33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is (C) Y₁ = ₁₂e + c₂e² + c3 (D) Ye=c₁e + c₂xе¯² + c3
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