There are two ways (at least) of doing this the first involves differentiating one of the equation and then substituting the other into the new equation:

Then solving the new equation for \dot y:

Laplace transforming:

Applying the initial conditions , this becomes:

which you invert by the use of partial fractions and a table of inverse Laplace transforms.

The second method involves writing this as a vector ODE:

where:

and:

Now take the Laplace transform:

Then (as : )

Now with some matrix algebra you can find and and proceed as before.

CB