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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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Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Campbell University

Idaho State University

Boston College

Lectures

13:37

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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01:22

Solve the equation $e^{-y}…

01:05

Solve the equation $e ^ { …

03:00

Solve the differential equ…

07:27

01:24

Solve the equation $y ^ { …

02:29

Solve the equation $y^{\pr…

05:48

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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