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56) Which function f(x) = Σar" satisfies the differential equation 1-0 f'(x) = -2xf(x)? a) f(x) = b) f(x)= c) f(x) = d) f(x)= (-1)" n=0 ∞ 2 (-1)" (2n)! n=0 (-1)"-12-1 n! n=0 (-1)-12 (-1)n-121 n=0 None of the shou

56) Which function f(x) = Σar" satisfies the differential equation 1-0 f'(x) = -2xf(x)? a) f(x) = b) f(x)= c) f(x) = d) f(x)= (-1)" n=0 ∞ 2 (-1)" (2n)! n=0 (-1)"-12-1 n! n=0 (-1)-12 (-1)n-121 n=0 None of the shou

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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56) Which function f(x) = Σana" satisfies the differential equation 72=0 f'(x) = -2xf(x)? a) f(x) = - b) f(x) = - c) f(x) = n=1 b) Σ - Σ d) f(x) = (-1)^-1 n=0 e) None of the above. 57) Which of the following series converge? 00 a) b) (-1)" (- (-1)" (2) (-1)"-12-1 n=0 n=0 n² + 2 n³-n+5 c) Σ(-1)"+¹ sin() n=1 n²+2 n³n+5 d) (-1)"+¹ cos() n=1 e) None of the above. 58) Which of the following statements are true? 1 LI 1+x11dx = " arctan(a®de>! c) The power series n=0 a) -18° C b) -20° C c) -22° C d) -26° C e) -32° C n=0 (1)11+1 11n +1 a) e 2 b) - 2 c) e-4 d) el-2 e) None of the above. 0.001 3 d) The power series has radius of convergence R = 0. n=0 e) If f)(0) = 0 for all k = 0, 1, 2, 3, ..., then f(x) = 0 for all x € R. n157n6+14n² +3 n19+2n12+34n6 +82" has radius of convergence R = 1. 44) Assume that f(x) is a solution to the differential equation y'= 2x + y with f(0) = -1. Then f(1) =? 45) An object at an unknown temperature is placed in a room which is held at a constant temperature of 5º C. If after 10 minutes the temperature of the object is -15° C and after 20 minutes the temperature of the object is -10° C, the unknown initial temperature of the object is approximately:
Transcribed Image Text:56) Which function f(x) = Σana" satisfies the differential equation 72=0 f'(x) = -2xf(x)? a) f(x) = - b) f(x) = - c) f(x) = n=1 b) Σ - Σ d) f(x) = (-1)^-1 n=0 e) None of the above. 57) Which of the following series converge? 00 a) b) (-1)" (- (-1)" (2) (-1)"-12-1 n=0 n=0 n² + 2 n³-n+5 c) Σ(-1)"+¹ sin() n=1 n²+2 n³n+5 d) (-1)"+¹ cos() n=1 e) None of the above. 58) Which of the following statements are true? 1 LI 1+x11dx = " arctan(a®de>! c) The power series n=0 a) -18° C b) -20° C c) -22° C d) -26° C e) -32° C n=0 (1)11+1 11n +1 a) e 2 b) - 2 c) e-4 d) el-2 e) None of the above. 0.001 3 d) The power series has radius of convergence R = 0. n=0 e) If f)(0) = 0 for all k = 0, 1, 2, 3, ..., then f(x) = 0 for all x € R. n157n6+14n² +3 n19+2n12+34n6 +82" has radius of convergence R = 1. 44) Assume that f(x) is a solution to the differential equation y'= 2x + y with f(0) = -1. Then f(1) =? 45) An object at an unknown temperature is placed in a room which is held at a constant temperature of 5º C. If after 10 minutes the temperature of the object is -15° C and after 20 minutes the temperature of the object is -10° C, the unknown initial temperature of the object is approximately:
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