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6. For the differential equation z²y" + xy-y=0 (a) Show that y₁(z) = z and y₂(x) = are two linearly independent solutions of the equation (b) Write the general solution of the differential equation (e) Solve the initial value problem with y(1) = 1 and y′(1) = −1 (d) On what interval is this a solution valid?

6. For the differential equation z²y" + xy-y=0 (a) Show that y₁(z) = z and y₂(x) = are two linearly independent solutions of the equation (b) Write the general solution of the differential equation (e) Solve the initial value problem with y(1) = 1 and y′(1) = −1 (d) On what interval is this a solution valid?

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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6. For the differential equation z²y" + xy - y = 0 (a) Show that y₁ (2) = 2 and y₂(x) = are two linearly independent solutions of the equation (b) Write the general solution of the differential equation (c) Solve the initial value problem with y(1) = 1 and y'(1) = −1 (d) On what interval is this a solution valid?
Transcribed Image Text:6. For the differential equation z²y" + xy - y = 0 (a) Show that y₁ (2) = 2 and y₂(x) = are two linearly independent solutions of the equation (b) Write the general solution of the differential equation (c) Solve the initial value problem with y(1) = 1 and y'(1) = −1 (d) On what interval is this a solution valid?
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