a.Assuming a, b, and k are constants, calculate the following derivative: (d/dt)( [ [a],[b] ]ekt = ? b.Find a value k so that [[1],[1]]ekt is a solution to x'= [[1,3],[3,1]]x. k = ? c.Find a value k so that [[1],[-1]]ekt is a solution to x'= [[1,3],[3,1]] k=? d.Write down a general solution in the form x1(t)=? and x2(t)=? , i.e., write down a formula for each component of a solution. Use A and B to denote arbitrary constants. The A should go with the first k you found above, and B should go with the second k you found above. x1(t)= ? x2(t)=? Whenever I use brackets I am denoting a matrix since I cannot copy and paste it, most of the matrixes, are vertical
a.Assuming a, b, and k are constants, calculate the following derivative: (d/dt)( [ [a],[b] ]ekt = ? b.Find a value k so that [[1],[1]]ekt is a solution to x'= [[1,3],[3,1]]x. k = ? c.Find a value k so that [[1],[-1]]ekt is a solution to x'= [[1,3],[3,1]] k=? d.Write down a general solution in the form x1(t)=? and x2(t)=? , i.e., write down a formula for each component of a solution. Use A and B to denote arbitrary constants. The A should go with the first k you found above, and B should go with the second k you found above. x1(t)= ? x2(t)=? Whenever I use brackets I am denoting a matrix since I cannot copy and paste it, most of the matrixes, are vertical
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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a.Assuming a, b, and k are constants, calculate the following derivative:
(d/dt)( [ [a],[b] ]ekt = ?
b.Find a value k so that [[1],[1]]ekt is a solution to x'= [[1,3],[3,1]]x.
k = ?
c.Find a value k so that [[1],[-1]]ekt is a solution to x'= [[1,3],[3,1]]
k=?
d.Write down a general solution in the form x1(t)=? and x2(t)=? , i.e., write down a formula for each component of a solution. Use A and B to denote arbitrary constants. The A should go with the first k you found above, and B should go with the second k you found above.
x1(t)= ?
x2(t)=?
Whenever I use brackets I am denoting a matrix since I cannot copy and paste it, most of the matrixes, are vertical matrixes.
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