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Problem

Solve the differential equation. $ t \ln t \frac…

02:07

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Problem 13 Medium Difficulty

Solve the differential equation.
$ t^2 \frac {dy}{dt} + 3ty = \sqrt {1 + t^2}, t > 0 $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 5

Linear Equations

Related Topics

Differential Equations

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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.

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Watch More Solved Questions in Chapter 9

Problem 1
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Problem 5
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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

In order to solve this equation, we must first get into the standard form. Why? Prime plus p of x times. Why is Q backs and orgy this? We must divide by t squared to get this into the standard form that I just mentioned. So as I said, I'm dividing by t squared. Okay, Now that we've got this, we know we must determine the integrating factor. Each of the integral of three over tee times D t is the same thing has eaten the three, not a log of tea which is the same thing as eat the natural of t cubed. Now we know eats the natural log is once this the same thing as t cubed. We have just determined are integrating factor. Okay, Now we must multiply both sides. In other words, all terms by the integrating factor that we just determined in order to know integrate both sides and sulfur Why we have t cubed. Why is the integral of tea times one plus she squared d t which gives us t cubed. Why is one third times one plus t squared 23 over to pussy We use the power room or to do this other words. We increased our expert by one and we then divided by the new exponents. Lastly, we only want this in terms of why not any sort of co fishing in front? That isn't one, which means we must divide by t cubed for the terms in order to derive our final solution plus c times t to the negative three which the same thing is pussy over too cute.

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Related Topics

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Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

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
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