Question

Let {y1, y2} be a set of fundamental solutions to the differential equation y'' + p(x)y' + q(x)y = 0. Then: (i) The Wronskian of y1, y2 is nonzero everywhere. (ii) y1, y2 are linearly dependent. (iii) y = c1y1 + c2y2 is the general solution. a. Only (iii) is true. b. Only (i) and (iii) are true. c. Only (ii) and (iii) are true. d. All are true.

Name: 1 let y1y2 be a set of fundamental solutions to the differential equation ypxyqxy0 then i the wronskian of y1y2 is nonzero everywhere ii y1y2 are linerar dependent iii yc1y1c2y2 is the gener 44025
Uploaded: 2023-08-02T14:18:23-08:00
Duration: 3 min 40 s
Channel: Madhur L
Description: 1 let y1y2 be a set of fundamental solutions to the differential equation ypxyqxy0 then i the wronskian of y1y2 is nonzero everywhere ii y1y2 are linerar dependent iii yc1y1c2y2 is the gener 44025

          Let {y1, y2} be a set of fundamental solutions to the differential equation y'' + p(x)y' + q(x)y = 0. Then:
(i) The Wronskian of y1, y2 is nonzero everywhere.
(ii) y1, y2 are linearly dependent.
(iii) y = c1y1 + c2y2 is the general solution.

a. Only (iii) is true.
b. Only (i) and (iii) are true.
c. Only (ii) and (iii) are true.
d. All are true.

Added by F-Tima R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/02/2023

Step 1

Explanation: (i) The Wronskian of y1,y2 is nonzero everywhere because it is given by W(y1,y2) = y1y2' - y1'y2, and if y1 and y2 are fundamental solutions, then they are linearly independent, which means that their Wronskian is nonzero. (ii) y1,y2 are linearly Show more…

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Let {y1, y2} be a set of fundamental solutions to the differential equation y'' + p(x)y' + q(x)y = 0. Then: (i) The Wronskian of y1, y2 is nonzero everywhere. (ii) y1, y2 are linearly dependent. (iii) y = c1y1 + c2y2 is the general solution. a. Only (iii) is true. b. Only (i) and (iii) are true. c. Only (ii) and (iii) are true. d. All are true.