What is the transfer function of this system of differential equations?

$2\frac{d^2y_1(t)}{dt^2} + 2\frac{dy_1(t)}{dt} + 1+2y_1(t) - 2\frac{dy_2(t)}{dt} = 0 $

$2\frac{d^2y_2(t)}{dt^2} + 2\frac{dy_2(t)}{dt} - 2\frac{dy_1(t)}{dt}=f(t)$

Where f(t) is the input
and y_2(t) is the output

I previously tried to find the transfer function by first applying Laplace transform, then substituting Y_1(s) in terms of Y_2(s) into the second equation and rearranging. The transfer function I found using this method was 4th order, had a ^-1 term in the denominator and just didn't look right to me.

If anyone can tell me what the transfer function should look for this system it would be greatly appreciated.
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