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$$y^{\prime \prime}+y=0$$

$y(t)=c_{1} \cos t+c_{2} \sin t$

Calculus 2 / BC

Chapter 4

Linear Second-Order Equations

Section 3

Auxiliary Equations with Complex Roots

Differential Equations

Missouri State University

Oregon State University

Baylor University

University of Nottingham

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.

33:32

10:31

$y^{\prime \prime}+y=0$

07:19

$y^{\prime}-y=0$

08:14

$y^{\prime \prime}-2 y^{\p…

01:04

$y^{\prime \prime}+x y=0…

05:12

$y^{\prime \prime \prime}-…

02:55

$$y^{\prime \prime}+y=0 ; …

Okay, we have wire, double prime. That's why is equal to zero. So this is the equation for a simple harmonic oscillator, so we couldn't get that. The characters equation is R squared, plus one equals zero, she replies. That are is a good place for minutes I. So why have tea? It's going to simply be C one, of course, NT. Let's see two times Scientist based on the complex roots.

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4. $$y^{\prime \prime}+2 y^{\prime}+y=e^{-t}$$

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