l88 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



tions of any of these differential equations. The range in x is i to 10; in 

 a, +0.5 to +4.0 and -0.5 to -3.0; in 7, i to 7. For negative values of x the 

 equations of 8.61 may be used. 



SPECIAL DIFFERENTIAL EQUATIONS 



8.700 



where X(x) is any function of x. The complete solution is: 



i /** 



y = Cl e nx + c 2 e- nx + - I X(%) sinh n(x - Q d%. 



8.701 



The complete solution, satisfying the conditions: 



x = o y = y<>, 



d y .. / 





y = 



where 

 8.702 



, sin w'# / , K . , \ 1 

 - -, -- h ^o (cos nx H -- 7 sin n x J > 



I - K* 



w' = V 2 --- 

 4 



/ crSfWdx 



J fe-SWg(x)dx 



egxx Cl + 

 8.703 



/ 

 ; - 

 [Cl~ 



8.704 



/efo 

 Ci-S*r 



