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In Exercises 25-36, find the solution of the given initial value problem. "+10y' +25y = 0, y(0)=2, y'(0) = 110

In Exercises 25-36, find the solution of the given initial value problem. "+10y' +25y = 0, y(0)=2, y'(0) = 110

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 A₁ and A₂. A fundamental set of solutions is 3₁ (t) = edit and 32(1) = ¹2. • If p² - 4q = 0, the characteristic equation has one repeated real root λ. A fundamental set of solutions is 3₁ (t) = et and Y2(t) = text. If p²-4q <0, the characteristic equation has two complex con- jugate roots a ±ib. A fundamental set of solutions is y(t) = el cos bt and y2(t) = eat sin bt. . . In Exercises 25-36, find the solution of the given initial value problem. J" +10y' +25y = 0, y(0)=2, y'(0) = -1 2
Transcribed Image Text:This information can be summarized as follows: If p²-4q> 0, the characteristic equation has two distinct, real roots A₁ and A₂. A fundamental set of solutions is 3₁ (t) = edit and 32(1) = ¹2. • If p² - 4q = 0, the characteristic equation has one repeated real root λ. A fundamental set of solutions is 3₁ (t) = et and Y2(t) = text. If p²-4q <0, the characteristic equation has two complex con- jugate roots a ±ib. A fundamental set of solutions is y(t) = el cos bt and y2(t) = eat sin bt. . . In Exercises 25-36, find the solution of the given initial value problem. J" +10y' +25y = 0, y(0)=2, y'(0) = -1 2
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