/*! 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} Q16E find a differential operator tha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q16E (page 337)

find a differential operator that annihilates the given function.

x2-ex

Short Answer

Expert verified

D4-D3is the differential operator that annihilates the given function.

Step by step solution

01

Differentiate the function continuously

Let the function bef(x)=x2-ex

Letg(x)=x2

Then

g'(x)=2xg''(x)=2g'''(x)=0D3[g]=0

Leth(x)=-ex

Then

h'(x)=-exh'(x)-h(x)=0(D-1)[h]=0

HenceD3(D-1)[f]=0

Then D4-D3is the differential operator that annihilates the given function.

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

Determine whether the given functions are linearly dependent or linearly independent on the interval(0,鈭�) .

(a){e2x,x2e2x,e-x}

(b){exsin2x,xexsin2x,ex,xex}

(c) {2e2x-ex,e2x+1,e2x-3,ex+1}

Find a general solution for the differential equation with x as the independent variable:

u'''鈭�9u''+27u'鈭�27u=0

find a general solution to the given equation. y'''+y''-5y'+3y=e-x+sinx.

. find a differential operator that annihilates the given function.

xe-2x+xe-5xsin3x

find a general solution to the given equation.

y'''+3y''-4y=e-2x
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.