35. Let the assumed particular solution for the given DE be yp = (Ar³ + Br² + Cx)e² + E. What is the value of A? (A) (B) (c) // (D) - -/
35. Let the assumed particular solution for the given DE be yp = (Ar³ + Br² + Cx)e² + E. What is the value of A? (A) (B) (c) // (D) - -/
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
ANSWER 35-40 ONLY PLEASE THANK YOU
Transcribed Image Text:36. Let the assumed particular solution for the given DE be yp = (Ax³ + Br² + Cx)e² + E. What is
the value of C?
/
(B)
(A) 5
6
37. Let the assumed particular solution for the given DE be yp = (Ar³ + Br² + Ca)e² + E. What is
the value of E?
(B) -5
(A)
(B)
38. Consider the differential equation: y" + 4y = g(x), g(x) 0. Using the method of undetermined
coefficients, which of the following can be the form of the assumed particular solution for the given
DE if g(x) = 4 cos x - 3 sin x - 8.
(A) y₂ = Ar cos x + Bxsin x + E, where A, B, E are arbitrary constants to be eliminated.
(B) Yp7
= Ae² cos x + Be² sin x + E, where A, B, E are arbitrary constants to be eliminated.
(C) yp = Ax² cos x + Br² sinr + E, where A, B, E are arbitrary constants to be eliminated.
(D) yp = A cos 2x + B sin 2x + E, where A, B, E are arbitrary constants to be eliminated.
39. Evaluate L{et cos 6t}
s-2
s² - 4s + 40
s-2
s²-4s-32
40. Evaluate L-1
(A) cos
(B) sin
(c)
(D) -
71272
4s
(c)
(D) -
4s²
(C)
(D)
6
s² - 4s + 40
6
s² - 4s
(C) cosh;
(D) sinh
12412
32
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)^(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)
32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the
DE y" + 2y" - y = 10 are
(A) Y₁ = C₁e + C₂€¯² + c3
(B) Ye=C₁e + C₂xE² + c3
(C) D¹(D² - 1)³(D² +9)²
(D) D¹(D²+1)³(D² - 9)²
(C) - 2r
(D) -2
33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is
(A) Ye=c₁e + ₂xе-²
(B) Ye=c₁e +₂2₂e²
(C) m = 0,-1 (multiplicity 2)
(D) m = 1,-1 (multiplicity 2)
(A)
(B) –
For the next four questions, consider the differential equation: y" - y = x²e² - 5
(C) Ye=c₁e + c₂e² + C3
(D) Ye=c₁e + C₂xе¯² + c3
34. Which of the following represents the complementary function for the given DE?
(C) =ce* +Gre
(D) ye = ₁x + ₂xе-²
35. Let the assumed particular solution for the given DE be yp = (Ar³ + Br² + Ca)e² + E. What is
the value of A?
(c) //
(D) -
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