Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q22E (page 164)

In Problems 22–25, use the method described in Problem 21to find a general solution to the given equation.

22. 3Y' - 7Y = 0

Short Answer

Expert verified

The general solution is y(t)=ce73t.

Step by step solution

01

Substitute y = ert

The given differential equation is 3y' - 7y = 0

Substitutey = ert and y' = rert,

3(rert)-7(ert)=0(3r-7)(ert)=03r-7=0r=73

02

Find the general solution.

Therefore y(t)=e73t.

Thus, the general solution is y(t)=ce73t.

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

Find a general solution y''-y'+7y=0

Prove the sum of angles formula for the sine function by following these steps. Fix x.

(a)Let f(t)=sin(x+t). Show that f''(t)+f(t)=0, the standard sum of angles formula forsin(x+t) .f(0)=sinx , and f'(0)=cosx.

(b)Use the auxiliary equation technique to solve the initial value problem y''+y=0,y(0)=sinx, andy'(0)=cosx

(c)By uniqueness, the solution in part(b) is the same as following these steps. Fix localid="1662707913644" x.localid="1662707910032" f(t) from part (a). Write this equality; this should be the standard sum of angles formula for sin(x+t).

Determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y''-y'-12y=2t6e-3t

Find a particular solution to the differential equation.

2x'+x=3t2

Find a particular solution to the differential equation.4y''+11y'-3y=-2te-3t
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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