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Q4.3-11E

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Fundamentals Of Differential Equations And Boundary Value Problems

Found in: Page 172

Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

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Short Answer

Find a general solution $z " + 10 z' + 25 z = 0$

The general solution of the given equation $z " + 10 z' + 25 z = 0$ is $y (t) = (c_{1} + c_{2} t) e^{- 5 t}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information.

Given differential equation is $z " + 10 z' + 25 z = 0$ .

Step 2: Finding roots of the auxiliary equation.

Then the auxiliary equation is $r^{2} + 10 r + 25 = 0$

Solve the auxiliary equation to obtain the roots.

${(r + 5)}^{2} = 0 r + 5 = 0 r = - 5$

Step 3: Final answer.

Therefore, the general solution is $y (t) = (c_{1} + c_{2} t) e^{- 5 t}$

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