Chapter 8.9, Problem 31P

Solve the following sets of equations by the Laplace transform method.

$y^{\prime \prime }+z^{\prime \prime }-z^{\prime }=0$     $y_0=0,y_0^{\prime }=1$     $y^{\prime }+z^{\prime }-2z=1-e^t$     $z_0=1,z_0^{\prime }=1$