MATH 214 Worksheet 15 December 1, 2025
Problem 1. Consider the first-order system of differential equations given by
x0(t) = 4−2
8−4x(t) = Ax.
(a) Find the eigenvalues and eigenvectors of A.
(b) Find the general solution to the first order system.
(c) Given initial conditions x(0) = x1(0)
x2(0)=3
−1, find the solution to the initial value
problem.
Problem 2. Consider the first-order system of differential equations given by
x0(t) = 1−1
1 3 x(t) = Ax.
(a) Find the eigenvalues and eigenvectors of A.
(b) Find the general solution to the first order system.
(c) Given initial conditions x(0) = x1(0)
x2(0)=2
4, find the solution to the initial value
problem.
Problem 3. Consider the first-order system of differential equations given by
x0(t) = 1−4
4−7x(t) = Ax.
(a) Find the eigenvalues and eigenvectors of A.
(b) Find the general solution to the first order system.
(c) Compute the Wronskian of the pair of solutions you found in part (b).
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