Conway—The Partial Differential Equations of Mathematical Physics. 
We write this solution 
ff dudvf(u + v)[w? — re) [0? — p72) = Kaa) 4m (% p); 
and it can obviously be expressed in various ways as a sum of functions 
Kin-2); or ot EG toys 
VI.—Non-Homocentous EQuaTIons. 
By a linear substitution, the equation can be written in the form 
ap , op ob 
ane ste ae GP 00 ¢ ay? — oP ch = 0. 
If a does not vanish, by the substitution 
L Y 
p= e° 2a" Ww, 
we get 
al ony on 
ae =o 6 2 Oa stn (). 
197 
If c’=0, ve. if 0? =4ae, the equation is homogeneous. If ¢’ + 0, the equation 
to be solved is of the form 
If x =e, where & does not contain 7, and 7 is a new variable, then we 
have got to get a solution x of 
CaN Gy Ce OY CaN 
ZOCOR Rm Ay SS a oOo ae a 
02) 04, OT OY OY m 
such that e7x will not contain 7. 
Such a solution is 
pu? | edi = | oe i ee 
[(u a Tt) = a ROD (v? =x Pye)? 
and hence 
e’dv 
we pie | ae 
