Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Solve the initial-value problem. $ t \frac {du}{…

01:50

Question

Answered step-by-step

Problem 16 Medium Difficulty

Solve the initial-value problem.
$ t^3 \frac{du}{dt} + 3t^2y = \cos t, y(\pi) = 0 $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Amrita Bhasin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 5

Linear Equations

Related Topics

Differential Equations

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

13:37

Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Join Course
Recommended Videos

04:47

Solve the initial-value pr…

02:31

find the solution of the g…

01:34

Solve the initial-value pr…

08:02

Solve the given initial-va…

03:37

Verify that $ y = -t \cos …

02:31

Solve the initial-value pr…

Watch More Solved Questions in Chapter 9

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38

Video Transcript

to solve this initial value problem. The first thing they could do is divide each turn by CI Cube to get us into the standard form. Why? Prime plus p of x y is q of axe. So again, I'm dividing each term. Okay, Integrating factor. Each of the integral p of t d t. We know this integrates to eat the three natural log of t which is the same thing as eat the natural log of t cubed. Remember, each the not walk of is simply one which means we have t cubed is our integrating factor multiplying the differential equation by the intrigue factor In other words, each of the terms we end up with us now integrating both sides we can solve for why soul For why, by dividing each of these terms by t cubed order to get why is teach the negative three sign of tea costs each e to the negative three Now use the initial value. Why of pi zero In order find See we have zero is pied to the 93. Just think of this accident. Why, that's literally what we're doing. We're just plugging in our accent. Why values because again we're trying to solve for C, which is our constant of integration. We get zero is equivalent to see because 00 plus c pied to the negative three. So see a zero, which means our solution as why, as a sign of tea divided by t cubed.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
180
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
79
Hosted by: Alonso M
See More

Related Topics

Differential Equations

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

13:37

Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Join Course
Recommended Videos

04:47

Solve the initial-value problem. $t^{3} \frac{d y}{d t}+3 t^{2} y=\cos t, \qua…

02:31

find the solution of the given initial value problem. $$ y^{\prime}+(2 / t) y=(…

01:34

Solve the initial-value problem. $$t y^{\prime}+y=\sin t, y\left(\frac{\pi}{2}\…

08:02

Solve the given initial-value problem. $$y^{\prime}+2 y=u_{\pi}(t) \sin 2 t, \q…

03:37

Verify that $ y = -t \cos t - t $ is a solution of the initial value problem. …

02:31

Solve the initial-value problem. $$y^{\prime}+2 y \cos (2 t)=2 \cos (2 t), y\le…
Additional Mathematics Questions

02:49

a number consists of two digit of which tens digit exceeds the unit digit by…

00:17

Given 3 lines in the plane such that the points of intersection form a trian…

01:51

The equation for the pH of a substance is pH = –log[H+], where H+ is the con…

02:55

Express 2.015 ( bar on 15) in the form of fraction

01:19

on selling a mobile for 750,a shopkeeper loses 10%.For what amount should he…

02:41

if a simple interest on rs. 2000 increases by rs. 40 .when the rate % increa…

00:31

Floor of a room is to be fitted with square marble tiles of the largest poss…

00:44

The volume of a cube is 4.913 m .find the length of its edge

03:55

A conical pit of diameter 3.5 cm is 12m deep what is the capacity in KL?

01:34

if x is subtracted from both the numerator and denominator of 3/4, the resul…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started