BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Solve the initial-value problem.

22. 4y" – 20y' + 25y = 0, y(0) = 2, y'(0) = –3

To determine

To solve: The initial-value problem for differential equation 4y20y+25y=0 , y(0)=2 , y(0)=3 .

Explanation

Formula used:

Write the expression for differential equation.

ay+by+cy=0 (1)

Write the expression for auxiliary equation.

ar2+br+c=0 (2)

Write the expression for general solution of ay+by+cy=0 with same real roots.

y=c1erx+c2xerx (3)

Here,

r is the root of auxiliary equation.

Write the required differential formulae to evaluate the differential equation.

ddxenx=nenx

Consider the differential equation as follows.

4y20y+25y=0 (4)

Compare equation (1) and (4).

a=4b=20c=25

Find the auxiliary equation.

Substitute 4 for a , 20 for b and 25 for c in equation (2),

(4)r2+(20)r+(25)=04r220r+25=0(2r5)2=02r5=0

Simplify the equation as follows.

2r=5r=52

Find the general solution of 4y20y+25y=0 using equation (3).

Substitute 52 for r in equation (3),

y=c1e52x+c2xe52x (5)

Modify equation (5) as follows.

y(x)=c1e52x+c2xe52x (6)

Find the value of y(0)

Substitute 0 for x in equation (6),

y(0)=c1e52(0)+c2(0)e52(0)=c1e0+0=c1

Substitute 2 for y(0) ,

2=c1

Differentiate equation (6) with respect to x

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 17 Solutions

Show all chapter solutions add
Sect-17.1 P-11ESect-17.1 P-12ESect-17.1 P-13ESect-17.1 P-14ESect-17.1 P-15ESect-17.1 P-16ESect-17.1 P-17ESect-17.1 P-18ESect-17.1 P-19ESect-17.1 P-20ESect-17.1 P-21ESect-17.1 P-22ESect-17.1 P-23ESect-17.1 P-24ESect-17.1 P-25ESect-17.1 P-26ESect-17.1 P-27ESect-17.1 P-28ESect-17.1 P-29ESect-17.1 P-30ESect-17.1 P-31ESect-17.1 P-32ESect-17.1 P-33ESect-17.1 P-34ESect-17.2 P-1ESect-17.2 P-2ESect-17.2 P-3ESect-17.2 P-4ESect-17.2 P-5ESect-17.2 P-6ESect-17.2 P-7ESect-17.2 P-8ESect-17.2 P-9ESect-17.2 P-10ESect-17.2 P-11ESect-17.2 P-12ESect-17.2 P-13ESect-17.2 P-14ESect-17.2 P-15ESect-17.2 P-16ESect-17.2 P-17ESect-17.2 P-18ESect-17.2 P-19ESect-17.2 P-20ESect-17.2 P-21ESect-17.2 P-22ESect-17.2 P-23ESect-17.2 P-24ESect-17.2 P-25ESect-17.2 P-26ESect-17.2 P-27ESect-17.2 P-28ESect-17.3 P-1ESect-17.3 P-2ESect-17.3 P-3ESect-17.3 P-4ESect-17.3 P-5ESect-17.3 P-6ESect-17.3 P-7ESect-17.3 P-8ESect-17.3 P-9ESect-17.3 P-10ESect-17.3 P-11ESect-17.3 P-12ESect-17.3 P-13ESect-17.3 P-14ESect-17.3 P-15ESect-17.3 P-16ESect-17.3 P-17ESect-17.3 P-18ESect-17.4 P-1ESect-17.4 P-2ESect-17.4 P-3ESect-17.4 P-4ESect-17.4 P-5ESect-17.4 P-6ESect-17.4 P-7ESect-17.4 P-8ESect-17.4 P-9ESect-17.4 P-10ESect-17.4 P-11ESect-17.4 P-12ECh-17 P-1RCCCh-17 P-2RCCCh-17 P-3RCCCh-17 P-4RCCCh-17 P-5RCCCh-17 P-1RQCh-17 P-2RQCh-17 P-3RQCh-17 P-4RQCh-17 P-1RECh-17 P-2RECh-17 P-3RECh-17 P-4RECh-17 P-5RECh-17 P-6RECh-17 P-7RECh-17 P-8RECh-17 P-9RECh-17 P-10RECh-17 P-11RECh-17 P-12RECh-17 P-13RECh-17 P-14RECh-17 P-15RECh-17 P-16RECh-17 P-17RECh-17 P-18RECh-17 P-19RECh-17 P-20RECh-17 P-21RE

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Solve the equations in Exercises 112 for x (mentally, if possible). x+1=0

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 1-6, refer to the following figure, and determine the coordinates of each point and the quadrant i...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Test for divisibility by 2: 1205

Elementary Technical Mathematics

Solve each inequality. 9+16

Trigonometry (MindTap Course List)

Sketching a Line in the Plane In Exercises 35-42, sketch the graph of the equation. x+2y+6=0

Calculus: Early Transcendental Functions (MindTap Course List)

The maximum area in question 2 is ft2 20 ft2 25ft2 50 ft2 A carpenter has a 10-foot-long board to mark off a t...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th