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: 9781305756083

Author: James Stewart

Publisher: CENGAGE C

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 17.1, Problem 12E

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.1, Problem 11E

Chapter 17.1, Problem 13E

Students have asked these similar questions

K Find the x-values of all points where the function defined as follows has any relative extrema. Find the values of any relative extrema. f(x)=5x+ In x Select the correct choice below and, if necessary, fill in the answer boxes to complete your choices. OA. There is a relative minimum of OB. There is a relative maximum of OC. There is a relative minimum of OD. There are no relative extrema. at x= at x= at x= There is a relative maximum of at x=

21-100 Spring 2024 Fin gra 10 8 Ay -10 -B -2 -4- -6 -8- -10- 10 re xamp OK CH acer US

The total profit P(X) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x+6x² + 63x+1) (0≤x≤10). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit? a) The number of units that should be sold in order to maximize the total profit is ☐ (Simplify your answer.)

Chapter 17 Solutions

ACP CALCULUS UCI: MATH 2A/2B

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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

Solution Summary: The author explains the formula used to solve the differential equation.

Concept explainers

Videos

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

Want to see the full answer?

Chapter 17 Solutions