Exercise 4. (Complex Eigenvalues)Consider the system i = x – y, ÿ =x+y a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued). b) Write down the general solution for the system of differential equations using only real valued functions. [Hint: use the equality ewt – cos(wt) + i sin(wt)]

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Exercise 4.
(Complex Eigenvalues)Consider the system i = x – Y, ÿ = x+Y
a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they
will be complex valued).
b) Write down the general solution for the system of differential equations using only real
valued functions. [Hint: use the equality ewt = cos(wt) + i sin(wt)]
Transcribed Image Text:Exercise 4. (Complex Eigenvalues)Consider the system i = x – Y, ÿ = x+Y a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued). b) Write down the general solution for the system of differential equations using only real valued functions. [Hint: use the equality ewt = cos(wt) + i sin(wt)]
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