   Chapter 17, Problem 12RE

Chapter
Section
Textbook Problem

Solve the initial-value problem.12. y" – 6y' + 25y = 0, y(0) = 2, y'(0) = 1

To determine

To solve: The initial-value problem for differential equation y6y+25y=0 , y(0)=2 , y(0)=1 .

Explanation

Given data:

The differential equation is,

y6y+25y=0 (1)

Formula used:

Write the expression for a second order differential equation.

ay+by+cy=0 (2)

Write the expression for an auxiliary equation.

ar2+br+c=0 (3)

Write the expression for the complex roots.

r=α±iβ (4)

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

y(x)=eαx(c1cosβx+c2sinβx) (5)

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±b24ac2a (6)

Compare equation (1) and (2).

a=1b=6c=25

Substitute 1 for a, –6 for b, and 25 for c in equation (3),

(1)r2+(6)r+(25)=0r26r+25=0

Find the roots of auxiliary equation using equation (6).

Substitute 1 for a, –6 for b, and 25 for c in equation (6),

r=(6)±(6)24(1)(25)2(1)=6±361002=6±642=6±i82

r=3±i4 (7)

Compare equation (4) and (7)

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

Find the limit: limx1(2x2x+4).

Calculus: An Applied Approach (MindTap Course List)

In Exercises 516, evaluate the given quantity. log5125

Finite Mathematics and Applied Calculus (MindTap Course List)

Multiply: 1520320

Elementary Technical Mathematics

Evaluate the integral. 24. 01xx2dx

Single Variable Calculus: Early Transcendentals

The x-coordinate of the center of mass of the region bounded by , x = 1, x = 2, y = 0 is: ln 2 1 2 ln 2

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