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y" +10y' +25y = 0,

y" +10y' +25y = 0,

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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This information can be summarized as follows: If p²-4q> 0, the characteristic equation has two distinct, real roots A and A₂. A fundamental set of solutions is ₁ (t) = e^it and y(t) = et If p² - 4q = 0, the characteristic equation has one repeated real root λ. A fundamental set of solutions is y₁ (t) = et and y2(t) = te^t. • If p²-4q<0, the characteristic equation has two complex con- jugate roots a tib. A fundamental set of solutions is yi(t) = el cos bt and y2(t) = et sin bt. . In Exercises 25-36, find the solution of the given initial value problem. "+10y' +25y = 0,
Transcribed Image Text:This information can be summarized as follows: If p²-4q> 0, the characteristic equation has two distinct, real roots A and A₂. A fundamental set of solutions is ₁ (t) = e^it and y(t) = et If p² - 4q = 0, the characteristic equation has one repeated real root λ. A fundamental set of solutions is y₁ (t) = et and y2(t) = te^t. • If p²-4q<0, the characteristic equation has two complex con- jugate roots a tib. A fundamental set of solutions is yi(t) = el cos bt and y2(t) = et sin bt. . In Exercises 25-36, find the solution of the given initial value problem. "+10y' +25y = 0,
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