Fundamental Solution

Definition

A Fundamental Solution (Also called fundamental Set or Matrix) is a set of all linearly independent solutions which can express every possible solution of an ODE.

Example

The ODE:

$$y^{\prime \prime }+y=0$$

The general solution:

$$y(t)=c_1\cos (t)+c_2\sin (t)$$

The fundamental solution set:

$$\{\cos (t),\sin (t)\}$$

An example solution:

$$y(t)=2\cos (t)+3\sin (t)$$