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 in Exercise 9.2.2…

04:21

Question

Answered step-by-step

Problem 36 Easy Difficulty

Find a function $ f $ such that $ f(3) = 2 $ and
$ (t^2 + 1)f'(t) + [f(t)]^2 + 1 = 0 t \neq 1 $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Lucas Finney
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Lucas Finney

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 3

Separable Equations

Related Topics

Differential Equations

Discussion

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

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd 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

01:02

Find a function $f$ such t…

01:20

Find $ f $.

$ f&qu…

06:35

$$\begin{array}{l}{\text {…

03:24

Find the function $f$ such…

01:14

Find the function $f$ such…

03:58

Find the function $f$ such…

00:57

Find all functions $f(t)$ …

04:46

Find a function $f$ such t…

01:17

Find all functions $f(t)$ …

01:45

Find all functions $f(t)$ …

02:03

Find a function $f$ such t…

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
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54

Video Transcript

for this problem, we are asked to find a function apps such that f of three equals two and t squared plus F. Prime of T plus f of t squared plus one equals zero, where T does not equal one. So what we can do here is we want to set this up as a separable equation. So let's see here, we first and write this as f prime of T plus Let's see one moment. What we can do first is isolate the F prime of T onto one side. So we'd have F prime of T equals negative F squared minus one, divided by t squared plus one. Now to isolate our variables, we can divide both sides by negative x squared minus one. So we get F prime over negative x squared minus one is equal to one over T squared plus one. Now integrating the right hand side, The integral of that T squared plus one. Uh that is going to come out to one moment here, that's going to come out to arc tanne of T plus a constant. And then integrating the left hand side. There, we are going to get, I don't know, let me double check this one second. Yeah, if we integrate the left hand side, we just end up getting a negative arc tanne of F. So to isolate f We can multiply both sides by negative one and then take the tan of both sides. So we get that F is going to equal tan of negative arc tanne of T plus C. So the last step here is to solve for initial condition. So we want when T equals three. For this to equal to We need 10 of Negative Arc Tanne of three plus C. To equal to which then means that we can take the ark tan of both sides again. So we get that negative arc tanne of three plus C Needs to Equal Arc Tanne of two, which in turn means that we need C. Two equal arc tanne of two Plus Arc Tanne of three, and that's going to be the most precise way to communicate that.

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
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd 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

01:02

Find a function $f$ such that $f(1)=0$ and $f^{\prime}(x)=2^{\prime} / x$

01:20

Find $ f $. $ f"(t) = t^2 + 1/t^2 $, $ \quad t > 0 $, $ \quad f(2) = 3 $, $ …

06:35

$$\begin{array}{l}{\text { Find the function } f \text { such that } f^{\prime}…

03:24

Find the function $f$ such that $f^{\prime}(x)=f(x)(1-f(x))$ and $f(0)=\frac{1}…

01:14

Find the function $f$ such that $f ^ { \prime } ( x ) = f ( x ) [ 1 - f ( x ) ]…

03:58

Find the function $f$ such that $$f ^ { \prime } ( x ) = f ( x ) ( 1 - f ( x ) …

00:57

Find all functions $f(t)$ that satisfy the given condition. $$f^{\prime}(t)=t^{…

04:46

Find a function $f$ such that $f^{\prime \prime}(x)=(1+2 x)^{5}, f(0)=0$, and $…

01:17

Find all functions $f(t)$ that satisfy the given condition. $$f^{\prime}(x)=x, …

01:45

Find all functions $f(t)$ that satisfy the given condition. $$f^{\prime}(x)=2 x…

02:03

Find a function $f$ such that $f^{\prime \prime}(x)=6, f^{\prime}(-1)=2,$ and $…
Additional Mathematics Questions

00:35

Question 7
2 pts
Determine the general form of the equation of a line …

01:38

The equation of the ellipse that has a center at (3,4), a focus at (0,4), an…

02:50

Question 10
2 pts
Truck Rental Company rents out a moving truck for on…

08:11

2.) A cone of radius 2 cm and height 5 cm is lowered point first into a tall…

02:26

sure Jabel appropriatelly. Draw the image ofthe figure under the given rotat…

01:49

Find the measure of angle 3 in the given figure: %1 parallel to %, Angle 7 =…

02:18

Skttch ona tull perlod otho gruph of tra iunctlon #*

05:47

The lateral area of a circular cylinder is 120 ft2 and its volume is 300 ft?…

02:37

Do the figures below have rotational symmetry? Polnt symmetry? If a figure h…

03:11

Consider sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Prov…

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