Page 126 - Schaum's Outline of Differential Equations

CHAP. 12] VARIATION OF PARAMETERS 109

Solving this set of equations simultaneously, we obtain

whence

Then, from (_/),

and the general solution is

The solution also can be obtained simply by integrating both sides of the differential equation four times with
respect to x.

Supplementary Problems

Use variation of parameters to find the general solutions of the following differential equations:

In x if two solkution to the associated homogeneous problem are known to be x and 1/x

if two solution to the associated homogeneous problem are known to be I andex2.

2
if two solutions to the associated homogeneous equations are known to be t and i + 1.
12.24. if two solutions to the associated homogeneous equations are known to be
and

12.29. if three linearly independent solutions to the associated homogeneous equations are known to be
and

4-y(3) _ 32 g2*
12.30. y(S) _