206 
EXERCISES. 
10. (x + af^-4 (x + a) + % = 
11. Integrate — 2 bx — 0. 
12. A particular integral of (1 — af) —cc — a 2 y = 0 
is ?/ = (7e's' sin ~ 1 '* J find the complete integral "by the method of 
Art. 13. 
13. The form of the general integral might in the above 
case be inferred from that of the particular one without em 
ploying the method of Art. 13. Prove this. 
14. It being given that 
y 
— A (sina? + 
coscc 
x 
) + 4 
coscc ■ 
sm* 
X 
dSj 
is the complete integral of the equation + ^1 — 
find the general integral of ^ ~ — x *- 
15. Explain on what grounds it is asserted that the com 
plete integral of a differential equation of the n th order contains 
n arbitrary constants and no more. 
16. Mention any circumstances under which it may be 
advantageous to form, from a proposed differential equation, 
one of a higher order. In deducing from the solution of the 
latter that of the former, what kind of limitation must be 
introduced ?