system of differential equations

Does anybody know how to solve the system of differential equations,

y'(t) = -ay(t) + ax(t)

x'(t) = ay(t) -ax(t)

with initial conditions, y(0)=1 and x(0)=0 where a is a real constant and also with y(t) + x(t) = 1 for all t

Hi

Let's use the equations we're given : substitute in :



Hence is given by the ODE which you can solve. Once you know , you can use to find .