NOTE: Thus far we have assumed thatp(x)andq(x)iny′ +p(x)y = q(x)are continuous, yet in app...

NOTE: Thus far we have assumed thatp(x)andq(x)iny′ +p(x)y = q(x)are continuous, yet in applications that may not be the case. In particular, the “input”q(x)may be discontinuous. In Example 1, for instance,E(t)inLdi/dt + Ri = E(t)may well be discontinuous, such as

We state that in such cases, whereE(t)has one or more jump discontinuities, the solution (11) [more generally, (24) in Section 2.2] is still valid, and can be used in these exercises.

(RL circuit) For theRLcircuit of Example 1, withi0=0 andE(t) =Eq,determine the

time.required for i(t) to reach 99% of its steady-state value;