Consider the differential equation y" - y' - 12y = 0. Verify that the functions ex and ex form a fundamental set of solutions of the differential equation on the interval (-co, co). The functions satisfy the differential equation and are linearly independent since the Wronskian w(e-³x, e4x) - #0 for -∞0 < x < 00⁰. Form the general solution. Y = Show My Work (Required) What steps or reasoning did you use? Your work counts towards your score. e g MILICAL 244 9:17 11/9/
Consider the differential equation y" - y' - 12y = 0. Verify that the functions ex and ex form a fundamental set of solutions of the differential equation on the interval (-co, co). The functions satisfy the differential equation and are linearly independent since the Wronskian w(e-³x, e4x) - #0 for -∞0 < x < 00⁰. Form the general solution. Y = Show My Work (Required) What steps or reasoning did you use? Your work counts towards your score. e g MILICAL 244 9:17 11/9/
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:Consider the differential equation
y" - y' - 12y = 0.
Verify that the functions e-3x and e4x form a fundamental set of solutions of the differential equation on the interval (-co, co).
The functions satisfy the differential equation and are linearly independent since the Wronskian
w(e-3x, e4x) -
#0 for -∞0< x < 0.
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Form the general solution.
y =
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Show My Work (Required)?
What steps or reasoning did you use? Your work counts towards your score.
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