Consider the initial value problem j' = 3 j(0) = a. Form the complementary solution to the homogeneous equation. jc(t) = c1 + C2 b. Construct a particular solution by assuming the form p(t) = ä + bt and solving for the undetermined constant vectors ā and b. yp(t) = c. Form the general solution (t) = ýc(t) + ğp(t) and impose the initial condition to obtain the solution of the initial value problem. Y1(t) %3D y2(t)
Consider the initial value problem j' = 3 j(0) = a. Form the complementary solution to the homogeneous equation. jc(t) = c1 + C2 b. Construct a particular solution by assuming the form p(t) = ä + bt and solving for the undetermined constant vectors ā and b. yp(t) = c. Form the general solution (t) = ýc(t) + ğp(t) and impose the initial condition to obtain the solution of the initial value problem. Y1(t) %3D y2(t)
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:Consider the initial value problem
(0) =
a. Form the complementary solution to the homogeneous equation.
jct) = c1
+ C2
b. Construct a particular solution by assuming the form p(t) = ä + bt and solving for the undetermined constant vectors a and b.
yp(t) =
c. Form the general solution (t) = ýc(t) + ÿp(t) and impose the initial condition to obtain the solution of the initial value problem.
y1 (t)
y2(t)
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