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Consider the differential equation f(8) – 6 f(2) + 11f(1) – 6f = 0 We transform this differential equation into a system of differential equations by setting: = 9, = h and looking for the three functions f, f(1), f(2) at once, that is, for the vector (f, g, h)t consisting of three functions. We then have three equations that have the form: df = g dx dg h

Consider the differential equation f(8) – 6 f(2) + 11f(1) – 6f = 0 We transform this differential equation into a system of differential equations by setting: = 9, = h and looking for the three functions f, f(1), f(2) at once, that is, for the vector (f, g, h)t consisting of three functions. We then have three equations that have the form: df = g dx dg h

Advanced Engineering Mathematics
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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Consider the differential equation f(8) – 6f(?) + 11f(1) – 6ƒ = 0 We transform this differential equation into a system of differential equations by setting: 4 = g, = h and looking for the three functions f, f(1), f(2) at once, that is, for the vector (f,g,h)* consisting of three functions. We then have three equations that have the form: df = g dx dg = h dx dh = 6f – 11g +6h dx Solving this system solves the differential equation. Answer the following questions (Questions 1,2,3,4). Question 1 Write this system in matrix form as dv = Av where v = (f,g,h)*. Find the trace of the 3 x 3 matrix A and its determinant. The trace is the sum of its diagonal terms. O Trace=6, determinant=0 Trace=3, determinant=3 Trace=6, determinant=6 Trace=0, determinant=6
Transcribed Image Text:Consider the differential equation f(8) – 6f(?) + 11f(1) – 6ƒ = 0 We transform this differential equation into a system of differential equations by setting: 4 = g, = h and looking for the three functions f, f(1), f(2) at once, that is, for the vector (f,g,h)* consisting of three functions. We then have three equations that have the form: df = g dx dg = h dx dh = 6f – 11g +6h dx Solving this system solves the differential equation. Answer the following questions (Questions 1,2,3,4). Question 1 Write this system in matrix form as dv = Av where v = (f,g,h)*. Find the trace of the 3 x 3 matrix A and its determinant. The trace is the sum of its diagonal terms. O Trace=6, determinant=0 Trace=3, determinant=3 Trace=6, determinant=6 Trace=0, determinant=6
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