How can you tell Maple12 that A is constant?

Question

I have this equation

$$equation:=\frac{\partial ^{2}}{\partial t^2}x_1(t)=-2\omega^{2} x_1(t)+\omega ^2x_2(t)$$

Let's do substitutions:

$$x_1=A_1e^{i\omega t}$$ and $$x_2=A_2e^{i\omega t}$$

Now I would like to put these substitutions into our equation and convert it into

$$equationA:=(\omega ^2-2\omega ^2)A_1+\omega ^2A_2=0$$

The problem is that

$$\frac{\partial ^{2}}{\partial t^2}A_1e^{i\omega t}=-A_1\omega^2e^{i\omega t}$$

How to tell Maple that A is constant?

Answer 1

Eureka!!!!!!!!!!!!!!

See the picture below