Find a homogeneous linear differential equation with constant coefficients whose general solution is given by y=c1e−xcosx+c2e−xsinx.

Step-by-step explanation:

Given

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

Where

and

For a homogeneous linear differential equation, the repeated value m is given as:

Substitute values for and

Add 1 to both sides

Square both sides

In complex numbers:

So, the expression becomes:

Add 1 to both sides

This corresponds to the homogeneous linear differential equation

step-by-step explanation: