Page 129 - Schaum's Outline of Differential Equations

112 INITIAL-VALUE PROBLEMS [CHAP. 13

13.4. Solve
From Problem 10.1, we have

Since the given differential equation is homogeneous, y h is also the general solution. Applying each initial condition
separately, we obtain

Solving these equations simultaneously, we find

Substituting these values into the first equation (_/), we obtain

13.5. Solve
The general solution of the differential equation is given in Problem 12.5 as

Therefore,

Applying the first initial condition to (_/), we obtain

Hence c l = -1/6. Applying the second initial condition to (2), we obtain

Hence c 2 = 0. The solution to the initial-value problem is

13.6. Solve
The general solution of the differential equation and the derivative of the solution are as given in (_/) and (2)
of Problem 13.5. Applying the first initial condition, we obtain

or