In many physical problems the nonhomogeneous term may be specified by different

formulas in different time periods. As an example, determine the solution y = (t) of

y + y =

t, 0 t ,

et , t > ,

satisfying the initial conditions y(0) = 0 and y

(0) = 1. Assume that y and y are also continuous

at t = . Plot the nonhomogeneous term and the solution as functions of time.

Hint: First solve the initial value problem for t ; then solve for t > , determining the

constants in the latter solution from the continuity conditions at t = .