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Solve the equation $ y' = x \sqrt {x^2 + 1/(ye^y)} $ and graph several members of the family of solution (if your CAS does implicit plots). How does the solution curve change as the constant $ C $ varies?

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$e^{y}(y-1)=\frac{1}{3}\left(x^{2}+1\right)^{3 / 2}+C$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Oregon State University

Harvey Mudd College

Baylor University

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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Solve the equation $y^{\pr…

01:24

Solve the equation $y ^ { …

04:28

Solve the differential equ…

05:34

01:22

Solve the equation $e^{-y}…

07:27

03:00

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