Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Find the general solution of the given differential equation. Give the largest interval / over which the general solution is defined. Determine whether there are any transient terms in the general solution.

Short Answer

Expert verified

So, the solution of the given equation is.y=13+ce-4x;.

Step by step solution

01

Definition of transient term

A transient term means that you (or someone or something) will be moving on from where you are now.

02

Given data

Consider the following differential equation:

3dydx+12y=4

03

Evaluation

Dividing by 3, we get the standard form

dydx+4y=43

Multiplying the standard form by this factor, we get e4xdydx+4e4xy=43e4x, which is same as ddxe4xy=43e4x

On integration, we obtain

e4xy=13e4x+cy=13+ce-4x;orfor-<x<

ce-4xis a transient term, since, e-4x0asx.

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 Vaia!

One App. One Place for Learning.

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

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free