208 
EQUATIONS OF AN ORDER HIGHER 
A similar reduction may Ibe effected when x is wanting. 
Thus, if in the equation of the second order 
by means of which (4) becomes 
(5). 
Should we succeed by the integration of this equation of 
the first order in determining p as a function of y and c, sup 
pose p = (j> (y,c), the equation = p, will give 
whence 
(6). 
2. In close connexion with the above proposition, stand 
the three following important cases. 
Case I. When but one differential coefficient as well as 
but one of the primitive variables presents itself in the given 
equation.