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Solve the initial-value problem $ y' = (\sin x) \…

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Problem 24 Easy Difficulty

Solve the equation $ e^{-y}y' + \cos x = 0 $ and graph several members of the family of solutions. How does the solution curve change as the $ C $ varies?


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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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Top Calculus 2 / BC Educators
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Anna Marie Vagnozzi

Campbell University

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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.

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Watch More Solved Questions in Chapter 9

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Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
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Problem 15
Problem 16
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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

To the power 2 minus y, o s plus cos x, equals to 0. Therefore, it is to the power minus y dy over dx equals to minus cos x or is integration q to the power y dy is given as a question minus cos, x, d x. So, over all y over minus 1 equals to minus sine x, plus c. Therefore, we have 1 over the power y equal to sine x, minus c, or it is 1 over shine x, minus c equals to u to the power y. Therefore, we have l n sine x, minus c, inverse equal helen, the power y or we have y equals minus l, n, r, sine x, minus c. So this is the answer to the given.

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Calculus: Early Transcendentals

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Top Calculus 2 / BC Educators
Grace He

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Anna Marie Vagnozzi

Campbell University

Michael Jacobsen

Idaho 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
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