Page 141 - Schaum's Outline of Differential Equations

124 SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS [CHAP. 14

so the general solution is

The initial conditions are 7(0) = 0 and, from Eq. (14.8),

Applying the first of these conditions to (1) directly, we obtain

or Ci = - 40/17 = -2.35. Substituting this value into (1) and then differentiating, we find that

whereupon

and c 2 = 22.13. Equation (_/) becomes

14.16. Solve Problem 14.15 by first finding the charge on the capacitor.
Substituting the values given in Problem 14.15 into Eq. (14.5), we obtain

The associated homogeneous equation is identical in form to the one in Problem 1415, so it has the same solution
(with I h replaced by q h). Using the method of undetermined coefficients, we find a particular solution to be

so the general solution is

The initial conditions on the charge are q(0) = 0 and

Applying the first of these conditions to (_/) directly, we obtain

or Ci = -16/170 = - 0.0941. Substituting this value into (_/) and then differentiating, we find that