Explanation Formula used: Write the expression for differential equation. a y ″ + b y ′ + c y = 0 (1) Write the expression for auxiliary equation. a r 2 + b r + c = 0 (2) Write the expression for the complex roots. r = α ± i β (3) Write the expression for general solution of a y ″ + b y ′ + c y = 0 with complex roots. y = e α x ( c 1 cos β x + c 2 sin β x ) (4) Here, α is the real part of the root, and β is the imaginary part of the root. Write the expression to find the roots of quadratic equation . r = − b ± b 2 − 4 a c 2 a (5) Consider the differential equation as follows. d 2 R d t 2 + 6 d R d t + 34 R = 0 (6) Modify equation (1) as follows. a d 2 R d t 2 + b d R d t + c R = 0 (7) Compare equation (6) and (7). a = 1 b = 6 c = 34 Find the auxiliary equation. Substitute 1 for a , 6 for b and 34 for c in equation (2), ( 1 ) r 2 + ( 6 ) r + ( 34 ) = 0 r 2 + 6 r + 34 = 0 Find the roots of equation using equation (5)

8th Edition

ISBN: 9781337771474

Author: Stewart

Publisher: Cengage

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Differential Equations

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Chapter 17.1, Problem 12E

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To solve: The differential equation of d2Rdt2+6dRdt+34R=0 .

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Chapter 17.1, Problem 11E

Chapter 17.1, Problem 13E

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The differential equation of d 2 R d t 2 + 6 d R d t + 34 R = 0 .

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