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In Exercises 25-36, find the solution of the given initial value problem. y"-2y' +17y=0, y(0) = -2, y'(0)=3

In Exercises 25-36, find the solution of the given initial value problem. y"-2y' +17y=0, y(0) = -2, y'(0)=3

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 y₁ (t) = ₁ and 32(t) = e^2t If p² - 4q = 0, the characteristic equation has one repeated real root λ. A fundamental set of solutions is . ₁ (t) = et and 2(t) = te If p²-4g < 0, the characteristic equation has two complex con- jugate roots a tib. A fundamental set of solutions is y(t) = et cos bt and y2(t) = eat sin bt. In Exercises 25-36, find the solution of the given initial value problem. y"-2y+17y=0, y(0) = -2, y'(0)=3
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 y₁ (t) = ₁ and 32(t) = e^2t If p² - 4q = 0, the characteristic equation has one repeated real root λ. A fundamental set of solutions is . ₁ (t) = et and 2(t) = te If p²-4g < 0, the characteristic equation has two complex con- jugate roots a tib. A fundamental set of solutions is y(t) = et cos bt and y2(t) = eat sin bt. In Exercises 25-36, find the solution of the given initial value problem. y"-2y+17y=0, y(0) = -2, y'(0)=3
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