I am taking a beginner linear algebra class and would like a hint on a homework question. I don't need the answer, just a little guidance.

Consider the differential equation:

$\frac{{d}^{2}x}{d{t}^{2}}-\frac{dx}{dt}-x=\mathrm{cos}(t).$

We are told that the differential equation has a solution of the form

$x(t)=a\mathrm{sin}(t)+b\mathrm{cos}(t).$

Find $a$ and $b$, and graph the solution.

I don't know how to set up the system to use elimination to solve.

Consider the differential equation:

$\frac{{d}^{2}x}{d{t}^{2}}-\frac{dx}{dt}-x=\mathrm{cos}(t).$

We are told that the differential equation has a solution of the form

$x(t)=a\mathrm{sin}(t)+b\mathrm{cos}(t).$

Find $a$ and $b$, and graph the solution.

I don't know how to set up the system to use elimination to solve.