We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as dx/dt = −λ1x
dy/dt = λ1x − λ2y
dz/dt = λ2y
(which is discussed here) can be solved with no knowledge other than how to solve a single linear first order equation. Find a solution of the above system subject to the initial conditions x(0) = x0, y(0) = 0, z(0) = 0. (Assume that λ1 ≠ λ2.)