Differential Equations: An Introduction to Modern Methods and Applications
3rd Edition
ISBN: 9781118531778
Author: James R. Brannan, William E. Boyce
Publisher: WILEY

#### Videos

Textbook Question
Chapter 1.3, Problem 1P

In each of Problems 1 through 6 , determine the order of thegiven differential equation; also state whether the equation islinear or nonlinear.

t 2 d 2 y d t 2 + t d y d t + 2 y = sin t

To determine

The order of the differential equation t2d2ydt2+tdydt+2y=sint, and whether it is linear or not.

Solution:

The differential equation t2d2ydt2+tdydt+2y=sint is of the second order linear differential equation.

### Explanation of Solution

Given information:

The differential equation t2d2ydt2+tdydt+2y=sint.

The order of the highest derivative in an ordinary or partial differential equation is called the order of the differential equation.

For t2d2ydt2+tdydt+2y=sint, the highest order is 2.

The given differential equation is, therefore, of the second order.

An n th orderordinary differential equation of the form a0(t)y(n)+a1(t)y(n1)++an(t)y=g(t) is called linear. Where the functions a0,a1,...,an called the coefficients of the equation and they are dependent on t. The ordinary differential equation which is not in the above form is non-linear differential equation.

In the differential equation t2d2ydt2+tdydt+2y=sint, n=2, the coefficients a0(t)=t2,a1(t)=t,a2(t)=2 are dependent on t and g(t)=sint.

Therefore, the given differential equation islinear.

### Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
01:18

Find more solutions based on key concepts
a. The number of cube in the stack and number of face that are glued together.

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

Consider two investments, one earning simple interest and one earning compound interest. If both start with the...

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

The exponential form of the equation lnM=N by using base e.

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Knowledge Booster
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Calculus Volume 1
Math
ISBN:9781938168024
Author:Strang, Gilbert
Publisher:OpenStax College
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY