1. Use the Wronksian to verify the given functions form a fundamental set of solutions of the differential equation. Form the general solution. (Section 4.1) y" – 2y' + 5y = 0; e*cos 2x,e* sin 2x 2. Given y, is a solution to the differential equation, use reduction of order to find a second solution y2 (x). (Section 4.2) xy" +y' = 0; y1 = In x 3. Solve the initial-value problem. (Section 4.3) y" – 2y' + y = 0, y(0) = 5,y'(0) = 10
1. Use the Wronksian to verify the given functions form a fundamental set of solutions of the differential equation. Form the general solution. (Section 4.1) y" – 2y' + 5y = 0; e*cos 2x,e* sin 2x 2. Given y, is a solution to the differential equation, use reduction of order to find a second solution y2 (x). (Section 4.2) xy" +y' = 0; y1 = In x 3. Solve the initial-value problem. (Section 4.3) y" – 2y' + y = 0, y(0) = 5,y'(0) = 10
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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Transcribed Image Text:1. Use the Wronksian to verify the given functions form a fundamental set of solutions of the
differential equation. Form the general solution. (Section 4.1)
y" – 2y' + 5y = 0; e* cos 2x,e* sin 2x
2. Given y, is a solution to the differential equation, use reduction of order to find a second
solution y, (x). (Section 4.2)
ху" + у' %3D 0; у, %3DIn x
3. Solve the initial-value problem. (Section 4.3)
y" – 2y' + y = 0, y(0) = 5, y'(0) = 10
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