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3. Suppose a second order linear homogeneous equation y" + P(x)y' + Q(x)y = 0 has the following two solutions: Y1(x) = cos(x) + 5 sin(x), Y2(x) = e* sin(3x). a) Use Wrońskian determinent to decide whether y₁ and y2 are linearly independent. b) Find the solutions with the following initial conditions. i) y(0) = 1, y'(0) = 0 ii) y(0) = 0, y'(0) = 1 iii) y(0) = 22, y'(0) = 33

3. Suppose a second order linear homogeneous equation y" + P(x)y' + Q(x)y = 0 has the following two solutions: Y1(x) = cos(x) + 5 sin(x), Y2(x) = e* sin(3x). a) Use Wrońskian determinent to decide whether y₁ and y2 are linearly independent. b) Find the solutions with the following initial conditions. i) y(0) = 1, y'(0) = 0 ii) y(0) = 0, y'(0) = 1 iii) y(0) = 22, y'(0) = 33

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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3. Suppose a second order linear homogeneous equation y" + P(x)y' + Q(x)y = 0 has the following two solutions: Y1(x) = cos(x) + 5 sin(x), Y2(x) = e* sin(3x). a) Use Wrońskian determinent to decide whether y₁ and y2 are linearly independent. b) Find the solutions with the following initial conditions. i) y(0) = 1, y'(0) = 0 ii) y(0) = 0, y'(0) = 1 iii) y(0) = 22, y'(0) = 33
Transcribed Image Text:3. Suppose a second order linear homogeneous equation y" + P(x)y' + Q(x)y = 0 has the following two solutions: Y1(x) = cos(x) + 5 sin(x), Y2(x) = e* sin(3x). a) Use Wrońskian determinent to decide whether y₁ and y2 are linearly independent. b) Find the solutions with the following initial conditions. i) y(0) = 1, y'(0) = 0 ii) y(0) = 0, y'(0) = 1 iii) y(0) = 22, y'(0) = 33
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