coblem 2. Consider the system of linear differential equations for two real valued functions x(t) and y(t): Sx'(t) = -3x(t) – y(t) ly'(t) = x(t) – y (t) x(t) (a) Write the above system in matrix form X'(t) = AX(t), where X (t) = y(t) (b) Solve your system from part (a) to find two linearly independent vector solutions, 41(t) and 22(t). (c) Directly demonstrate that these two vector solutions e1 (t) and 42(t) are linearly indepen- dent (hint: examine the Wronskian determinant)
coblem 2. Consider the system of linear differential equations for two real valued functions x(t) and y(t): Sx'(t) = -3x(t) – y(t) ly'(t) = x(t) – y (t) x(t) (a) Write the above system in matrix form X'(t) = AX(t), where X (t) = y(t) (b) Solve your system from part (a) to find two linearly independent vector solutions, 41(t) and 22(t). (c) Directly demonstrate that these two vector solutions e1 (t) and 42(t) are linearly indepen- dent (hint: examine the Wronskian determinant)
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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Please solve c,d,e with the answer from a,b that be added in these picture
Transcribed Image Text:ols
370a-e2.pdf
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Problem 2. Consider the system of linear differential equations for two real valued functions x(t)
and y(t):
Sx'(t) = -3x(t) – y(t)
ly'(t) = x(t) – y(t)
(a) Write the above system in matrix form X'(t) = AX(t), where X (t) =
(b) Solve your system from part (a) to find two linearly independent vector solutions, P1(t) and
e2(t).
(c) Directly demonstrate that these two vector solutions 1(t) and 42(t) are linearly indepen-
dent (hint: examine the Wronskian determinant).
(d) Considering the initial conditions x(0) = 5 and y(0) = 2, find the particular solution to the
system of ODES in vector form, and then clearly state the component solutions x(t) and y (t).
(e) Plot x(t) and y(t) on the same axis and determine their end behaviors.
Problem 3. Consider the second-order linear ODE:
x"(t) +64x(t) = 0
where x(0) = ? and x'(0)
P Type here to search
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Transcribed Image Text:eiginvalue: h,= -2, =2
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General solution:
っX() - c, e^* + get*(in, +ve)
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