336 Chapter 11First-order differential equations
where(a 1 − 1 x),y, zand uare the amounts of A, B, C, and D, respectively, at time t. Given
the initial conditionsx 1 = 1 y 1 = 1 z 1 = 1 u 1 = 10 att 1 = 10 find the amount of C as a function of time.
Section 11.7
43.The current in an RL-circuit containing one resistor and one inductor is given by the
equation
Solve the equation for a periodic e.m.f.E(t) 1 = 1 E
0
1 sin 1 ωt, with initial conditionI(0) 1 = 10.
44.Show that the current in an RC-circuit containing one resistor and one capacitor is given
by the equation
Solve the equation for (i)a constant e.m.f.,E 1 = 1 E
0
, (ii)a periodic e.m.f.,E(t) 1 = 1 E
0
1 sin 1 ωt.
R
dI
dt
I
C
dE
dt
+=
L
dI
dt
+=RI E