d'y dy 2- dt Find the general solution to the ODE + 10y = 0. Enter solutions in alphabetical order. dt? y(t) = c1 * +c2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Differential Equations 

 

d'y
Find the general solution to the ODE
dt2
dy
+ 10y = 0. Enter solutions in alphabetical order.
dt
y(t) = c1
* +c2
Transcribed Image Text:d'y Find the general solution to the ODE dt2 dy + 10y = 0. Enter solutions in alphabetical order. dt y(t) = c1 * +c2
Expert Solution
Step 1

The given equation is d2ydt2-2dydt+10y=0

The auxiliary equation is D2-2D+10y=0

Solve for D

D2-2D+10=0D=--2±-22-411021=2±4-402=2±-362=2±6i2=1±3i

The roots are imaginary of the form α±βi therefore, the solution of the differential equation is given by

y=eαtc1cos βt+i sin βt

 

 

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