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Problem

Solve the differential equation $ y' = x + y $ by…

01:42

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Problem 20 Hard Difficulty

Find the function $ f $ such that $ f'(x) = xf(x) - x $ and $ f(0) = 2. $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 3

Separable 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 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
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Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54

Video Transcript

this question asked us to find the function f Such a f prime of X is X f of X minus acts and then given the fact that F zero is too now, first things first. We know we can right f prime of acts in terms of de roi de axe. It's easier to use why instead of F because then we can later on integrate our variables factor the right hand side to make it easier to divide. Now we can transfer all the Y terms over to the left hand side and all the ex terms over to the right hand side. Take the integral of both sides Integrate. Remember, we increased the extranet by one as you can see it from X to X squared and then we divide by the new exponents which is to ad see witches are constant integration. Remember that we're substituting x zero unwise to more solving for C so literally just substitute in our values To get rid of the variables and solve for C, we have zero equal see substitute sequel zero back in Now we know we're not done. Remember, the game plan is we need to get why equals? Which means we have to raise are based e We're raising the power to the base E on each equivalent side. So we have Y minus one is e to the X squared over to remember each. The Ellen is simply one. It just cancels. Now there's one last thing we have to do. Remember how the problem initially gave this in terms of F of X? Well, what this means is that we need to substitute why with FX, and then we will be flashed.

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Calculus: Early Transcendentals

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Related Topics

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Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

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
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Find the function $f$ such that $f^{\prime}(x)=x f(x)-x$ and $f(0)=2$.

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