set x_1 = y and x_2 = y' so that
x_1 ' = y' and
x_2 ' = y '' = y ' - 4y = x_2 - 4x_1
hence the given equation is equivalent to the system
X ' =
(-4 1) X
where X = [x_1 x_2] is a column vector.
The eigenvalues of the matrix ...
This provides an example of solving an ordinary differential equation as a system of first-order ordinary differential equations.