Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$$y^{\prime \prime}-10 v^{\prime}+26 y=0$$

$y(t)=c_{1} e^{5 t} \cos t+c_{2} e^{5 t} \sin t$

Calculus 2 / BC

Chapter 4

Linear Second-Order Equations

Section 3

Auxiliary Equations with Complex Roots

Differential Equations

Oregon State University

University of Michigan - Ann Arbor

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

03:09

$$y^{\prime \prime}-2 y^{\…

02:14

26. $$y^{\prime \prime}+2 …

00:49

$$y^{\prime \prime \prime}…

06:12

$y^{\prime \prime \prime}+…

05:48

$$y^{\prime \prime}-6 y^{\…

00:58

$$y^{\prime \prime}-5 y^{\…

01:53

$$y^{\prime \prime}+y^…

00:50

$$4 y^{\prime \prime}-4 y^…

okay, we have that are characteristic equation for this problem is R squared plus 26 minus 10 are is equal to zero. So once we solve this equation, we get that are is equal to five plus or minus I, which you can obtain using the quadratic formula. So why have team is equal to see one times each of the five p? Because that is our value here. Times Co sign of tea because of prohibition in front of the eyes, one plus C two times each, the five p sci fi, and this is to compensate for the complex, uh, complex part of this our value here.

View More Answers From This Book

Find Another Textbook

Numerade Educator

04:21

$$y^{\prime \prime \prime}+y^{\prime \prime}+3 y^{\prime}-5 y=0$$

01:54

$\frac{d^{2} w}{d t^{2}}+\frac{6}{t} \frac{d w}{d t}+\frac{4}{t^{2}} w=0$

06:07

$t^{2} \frac{d^{2} z}{d t^{2}}+5 t \frac{d z}{d t}+4 z=0$

06:16

Use the result of Problem 8 to prove that if the pendulum in Figure 4.18 on …

08:28

Pendulum Equation. To derive the pendulum equation (21), complete the follow…

02:22

$$y^{\prime \prime}-3 y^{\prime}-11 y=0$$

05:07

Given that $y_{1}(t)=(1 / 4) \sin 2 t$ is a solution to$y^{\prime \prime…

04:50

$y^{\prime}-y=1, \quad y(0)=0$

02:47

A garage with no heating or cooling has a time constant of 2 hr. If the outs…

04:31

$\theta^{\prime \prime}-\theta^{\prime}-2 \theta=1-2 t, \quad \theta_{p}(t)=…