. Acta Academiae scientiarum imperialis petropolitanae . a + y) X d dy -\-{y-\-?.)dy-\-^ + {2^ + Z)xddz+ (^4 ^)dz âo, IV. X dz\-{:i -h^)^- dz \-{^^<-\-^)xddz ^l^ ^^)dz\-a. x dy -\.{zaJ -\-y)x ddy-f (V+ £)=0, V. x d y ^ {6-\-a.) X d y -\-{6-\. i^ ci-\-y) X d^ y H- ( 2 a + 2 y + e) d dy -\ ^ x^ d\z + {^(i-\S)xdz-\ {2 (i+ 2^ + ^)ddzZZ0y VL X d z -\ {6 -^ (^y) x d z + {6 + ^(^1 + 6) X dz-+- ( 2 (3 + 2 5 + /) r/ // 2; â¢+ a .V d^y4-(d. a-{-y) X dy-\ {2 a-f 2 y-\ s) ddy:zo, VII. X dy -i-{9 4-a)-v ^/^ J + (i 8 4 ^ a + y) Jf ^^ + (6 + ^ a + 3 y + £) ^/ + p .V rf 2; + (6 |3 + 5) X ^/^ xr + (6
. Acta Academiae scientiarum imperialis petropolitanae . a + y) X d dy -\-{y-\-?.)dy-\-^ + {2^ + Z)xddz+ (^4 ^)dz âo, IV. X dz\-{:i -h^)^- dz \-{^^<-\-^)xddz ^l^ ^^)dz\-a. x dy -\.{zaJ -\-y)x ddy-f (V+ £)=0, V. x d y ^ {6-\-a.) X d y -\-{6-\. i^ ci-\-y) X d^ y H- ( 2 a + 2 y + e) d dy -\ ^ x^ d\z + {^(i-\S)xdz-\ {2 (i+ 2^ + ^)ddzZZ0y VL X d z -\ {6 -^ (^y) x d z + {6 + ^(^1 + 6) X dz-+- ( 2 (3 + 2 5 + /) r/ // 2; â¢+ a .V d^y4-(d. a-{-y) X dy-\ {2 a-f 2 y-\ s) ddy:zo, VII. X dy -i-{9 4-a)-v ^/^ J + (i 8 4 ^ a + y) Jf ^^ + (6 + ^ a + 3 y + £) ^/ + p .V rf 2; + (6 |3 + 5) X ^/^ xr + (6 (3 + 3 J + 2;) ^ 2=: o , VIII. xd z-i-{9-i-13) Jf ^ 2; + (; r 8 + 6 j3 + 5) xdz + {6 \ 6 p + 3 5 + <^) ^^ 2: + aX ^^j/ + (6 a + y) X dy + (6 «+ 3 y+ e) tf^j/ - o. Pro aequatione autem inuenienda , quae fola difFerentialiaipfins j inuoluat, fcquens fiat combinatio: VII. X-\ x\-{- VI. V X 4- III. |Jl A- +- IV. {JL X ^ tumque in aequatione refultante coefficientes differentia-*-lium ipfius y nihilo aequales ponantur x d x(Jy x d y x^ dy. x^ dy 5-i-6ii-{-3y-|-£+X(6+4a+y)+ f^(3 + a) + v ) 5^ ( X(2a+ 2 y + e)+ M.(2a+y)+va+X(2a+2y+e) I + \ (4 a +y) +|m.\ 2a+y) +va i + fi a ^*^^ + fx (y+ e)+ vy+fx(y+e)+ vy J?+ve |3+X jr ^ 2 X d d z \(2|3+2^ + <) +fA(2|3+J)+^/ G +X(2(3+2^+^ X d z + fx(^+<^) +.^)+fJL,S+^) +k(J + /< I 5(3 + 5 6(3+3J + <+ X(3 j + x(4|34^j X(6+(3)l+fx(3 + fx 1 4A(6+4|3+§)|+fji(2i3+5)+Kpl + P-(3+(3j + y| vnde fequentes refultant aequationes: |3+X=:o; 6 (3 + 5 + X (3 + X(5 + |3) + fxrr o; ^P+3 5 + i^:⬠) 57 ( Tbi A â
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