ä(t) – 7±(t) + 10x(t),= 0 x(0) = 2, ±(0) = 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 2. Find the solution of the following initial value problems.
i) #(t) – 7±(t) +10x(t),= 0 x(0) = 2, ±(0) = 3
ii) #(t) – 8å(t) + 25x(t) = 0, x(0) = 1, ±(0) = 0
iii) ä(t) – 9x(t) = 0, x(0) = 1, ¿(0) = 0
%3|
%3D
Problem 3. Rewrite the second order differential equation in Problem 2.i) and 2.ii) as a two
dimensional linear system of first order differential equations. Find the solutions for each of
these systems using linear system method. Verify that the solutions you obtain using the
linear systems method coincides with the approach you used in Problem 2.
Transcribed Image Text:Problem 2. Find the solution of the following initial value problems. i) #(t) – 7±(t) +10x(t),= 0 x(0) = 2, ±(0) = 3 ii) #(t) – 8å(t) + 25x(t) = 0, x(0) = 1, ±(0) = 0 iii) ä(t) – 9x(t) = 0, x(0) = 1, ¿(0) = 0 %3| %3D Problem 3. Rewrite the second order differential equation in Problem 2.i) and 2.ii) as a two dimensional linear system of first order differential equations. Find the solutions for each of these systems using linear system method. Verify that the solutions you obtain using the linear systems method coincides with the approach you used in Problem 2.
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