Consider the initial value problem i(0) = a. Form the complementary solution to the homogeneous equation. ýct) = c1 +C2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the initial value problem
-3
j' =
j(0) =
a. Form the complementary solution to the homogeneous equation.
ýct) = c1
+ C2
b. Construct a particular solution by assuming the form p(t) = (sin t)ā + (cos t)b and solving for the undetermined constant vectors ā and b.
ýp(t) =
c. Form the general solution (t) = jc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem.
y1(t)
5)
y2(t)
Transcribed Image Text:Consider the initial value problem -3 j' = j(0) = a. Form the complementary solution to the homogeneous equation. ýct) = c1 + C2 b. Construct a particular solution by assuming the form p(t) = (sin t)ā + (cos t)b and solving for the undetermined constant vectors ā and b. ýp(t) = c. Form the general solution (t) = jc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem. y1(t) 5) y2(t)
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