# Ordinary differential equation

Solve the ode y'' - y' +4y = 0 as a system of first order odes.

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#### Solution Preview

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 ' =

(0 1)

(-4 1) X

where X = [x_1 x_2] is a column vector.

The eigenvalues of the matrix ...

#### Solution Summary

This provides an example of solving an ordinary differential equation as a system of first-order ordinary differential equations.

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