We want to solve the homogeneous second-order linear differential equation d² y dx² (To input e*, type %e^x or exp (x).) +3 dy dx + 2 y = 0. First find the characteristic polynomial p(m) of this equation, by means of the trial solution y = emx: p(m) = Find the roots of this polynomial and use them to find the general solution to the differential equation: y = Now suppose that y = and = = when x = 0. Find the specific solution with these initial conditions: y =
We want to solve the homogeneous second-order linear differential equation d² y dx² (To input e*, type %e^x or exp (x).) +3 dy dx + 2 y = 0. First find the characteristic polynomial p(m) of this equation, by means of the trial solution y = emx: p(m) = Find the roots of this polynomial and use them to find the general solution to the differential equation: y = Now suppose that y = and = = when x = 0. Find the specific solution with these initial conditions: y =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:We want to solve the homogeneous second-order linear differential equation
y =
=
First find the characteristic polynomial p(m) of this equation, by means of the trial solution y
=
d² y
dx²
Now suppose that y = and =
11
3
dx
+3
(To input ex, type %e^x or exp(x).)
dy
(dr)
dx
p(m):
Find the roots of this polynomial and use them to find the general solution to the differential equation:
+ 2 y = 0.
emx:
when x = 0. Find the specific solution with these initial conditions: y =
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