190 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



8.711 



d?y 



dy 



y = (a + x] 



8.712 



// \n i 

 ~ U 

 ^ ' 



&y- 



d?y 2 dy t a 



A 4- LLr"V 



dx* + x dx ^ M y ~ x 1 



8.713 



= - j i cos IJLX + c 2 sin fjix + \ . 



dy 

 dx 



y = c l e~f )ix {p l sin fax + i) + Wi cos fax + 



+ c 2 e-P 2X \p 2 sin 

 where: 



cos 



2 + c - 



2P1 = J + \/Z- C + d 2 , 



and z is a root of 



z 3 - cz 2 - 4 (a 



M)z + 4(W - ad 2 - b 2 ) = o. 



(Kiebitz, Ann. d. Physik, 40, p. 138, 1913) 



