Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q4RP (page 1)

In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.

t3d3xdt32+3t-x=0

Short Answer

Expert verified

⦁ The Independent variable is t.

⦁ The dependent variable is x.

⦁ The equation is Non-Linear.

Step by step solution

01

Identifying the dependent and independent variables

Clearly, the independent variable is t while the dependent variable is x.

02

Determining whether the equation is linear or nonlinear

Since the third derivative has power 3, the equation is non-linear.

Hence, the Independent variable is t. The dependent variable is x. The equation is Non-Linear.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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 direction field for dydx=2x+yas shown in figure 1.13.

  1. Sketch the solution curve that passes through (0, -2). From this sketch, write the equation for the solution.

b. Sketch the solution curve that passes through (-1, 3).

c. What can you say about the solution in part (b) as x→+∞? How about x→-∞?

In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.

xd2ydx2+3x-dydx=e3x

In problems 1-4 Use Euler’s method to approximate the solution to the given initial value problem at the points x=0.1,0.2,0.3,0.4, and 0.5, using steps of size 0.1h=0.1.

dydx=-xy,y(0)=4

Let c >0. Show that the function ϕ(x)=(c2-x2)-1is a solution to the initial value problemdydx=2xy2,y(0)=1c2,on the interval-c<x<c. Note that this solution becomes unbounded as x approaches ±c. Thus, the solution exists on the interval(-δ,δ) with δ=c, but not for largerδ. This illustrates that in Theorem 1, the existence interval can be quite small (IFC is small) or quite large (if c is large). Notice also that there is no clue from the equationdydx=2xy2 itself, or from the initial value, that the solution will “blow up” atx=±c.

Nonlinear Spring.The Duffing equationy''+y+ry3=0 where ris a constant is a model for the vibrations of amass attached to a nonlinearspring. For this model, does the period of vibration vary as the parameter ris varied?

Does the period vary as the initial conditions are varied? [Hint:Use the vectorized Runge–Kutta algorithm with h= 0.1 to approximate the solutions for r= 1 and 2,

with initial conditionsy(0)=a,y'(0)=0 for a = 1, 2, and 3.]
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.

Sign-up for free