Compute the jacobian for non-autonomous system

Hi, I want to compute the Jacobian matrix for the following system:

x'=x1+x2*e^(-2t);

y'=-x1+x2;

I want to find the jacobian of this problem, without converting to the three dimensional problem.

I tried to compute the Jacobian using following code.

syms x y t

Ja=jacobian([x+y*exp^(-2*t);x+y], [x, y]);

I want to know whether this is the correct way to solve the problem.

Thank you.

[Kan Pri]

 x'=x1+x2*e^(-2t);
 y'=-x1+x2;