/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q3E A nonhomogeneous equation and a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q3E (page 186)

A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation.y''-y=t,鈥夆赌夆赌夆赌夆赌夆赌�yp(t)=-t

Short Answer

Expert verified

The general solution of the differential equation isy=c1et+c2e-t-t.

Step by step solution

01

Write the auxiliary equation of the given differential equation.

The differential equation is,

y''-y=t鈥夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆�夆赌夆赌夆赌夆赌夆赌夆�夆�夆��......(1)

Write the homogeneous differential equation of the equation (1),

y''-y=0

The auxiliary equation for the above equation,

m2-1=0

02

Now find the complementary solution of the given equation is

Solve the auxiliary equation,

m2-1=0m=卤1

The roots of the auxiliary equation are,

m1=1,鈥夆赌夆赌夆赌夆赌夆赌�m2=-1

The complementary solution of the given equation is,

yc=c1et+c2e-t

03

Use the given particular solution to find a general solution for the equation.

The given particular solution,

yp(t)=-t

Therefore, the general solution is,

y=yc(t)+yp(t)y=c1et+c2e-t-t

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The auxiliary equation for the given differential equation has complex roots. Find a general solution 4y''-4y'+26y=0.

Find a particular solution to the differential equation.

2x'+x=3t2

Determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y''-6y'+9y=5t6e3t

Vibrating Spring without Damping. A vibrating spring without damping can be modeled by the initial value problem(11)in Example3 by taking b=0.

a) If m=10kg,k=250kg/sec2,y(0)=0.3m, and y'(0)=-0.1m/sec, find the equation of motion for this undamped vibrating spring.

b)After how many seconds will the mass in part (a) first cross the equilibrium point?

c)When the equation of motion is of the form displayed in (9), the motion is said to be oscillatory with frequency 尾/2蟺. Find the frequency of oscillation for the spring system of part (a).

Find a general solution to the differential equation.

y''-2y'-3y=3t2-5
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.