(a-uf(y)dy For our particular problem we can now impose the boundary conditions u(0) a(1)=0 to determine the constants CI and C2. Thus, after some arithmetic, u(a) (1-x)f(y)y+/x(1-y)f(y)d u(a)=G(a, g)f(y)dy We note that G(a, y) has the following properties IS ·G(x,y)≥0 for all z,y∈(0,1 G is a piecewise linear function of a for fixed y and vice versa The particular form of expressing the solution, in terms of the green function will be revisited when we address the topic of integral equation Note 4 Consider an elastic bar of unit length which is fixed at both ends and subjected to a tangential load per unit length p(a) p() u(a) da➽❽➾❹➚✠➪➏➶➘➹❞➴✯➷⑩➹➏➬✂➚➨➮➳➱➳✃ ❐ ➾❹➚➨➮❊❒❩➪✶❮❽➾④❒♠➪✶❰✔❒↔Ï Ð❩Ñ✴Ò➏Ñ✴Ó❩Ò☛Ô✸Õ✱Ò❴Ö❴×❜Ø✚Ó❩Ù❜Õ✱Ò➏Ô❩Ò❡Ñ✔Ú❩Ù✙Û✪Ü➅Ý☛Û✢Ø✂Õ✱Þ➨Þ❩Ñ➎Ýß×✙Ü▲Ô❚Ñ➔à✶Û✥Ö❴á✸Û✥Ú✠Ñ✔Ó❩Þ❚â❩Õ✱Ò❡ãäØ✚Ñ✔Þ❚â♠×åÖ❡×✖Ñ✴Þ✸à ➽②➾✁æ✴➪ç➶ ➽❽➾❲è✌➪ç➶➌æ Ö❴Ñ➨â♠Û✪Ö❴Û✪Ò❡Ü▲×✖Þ✸Û✥Ö❡á❩Û❦Ø✚Ñ✴Þ✸à✶Ö❡Õ✱Þ➔Ö❙à ➹❪➴ Õ✔Þ✸â ➹☛➬✱é✯êá☎Ó✸à✂ë✸Õ➎ìíÖ❡Û✪Ò✒à❴Ñ✔Ü▲Û✤Õ✱Ò❡×åÖ❡á❩Ü▲Û✚Ö❴×❜Ø✱ë ➽②➾④➚✠➪✿➶ ➱✃ ❐ ❒✳➾✶è❞➮➺➚↔➪✶❮❽➾❹❒❩➪✶❰✔❒❦➷ ➱➋î ✃ ➚✞➾✶è✒➮➺❒❩➪❴❮❽➾❹❒❩➪❲❰✴❒↔ï Ñ✔Ò ➽❽➾❹➚↔➪✯➶ ➱ ➴ ❐⑧ð➾④➚❁ï✶❒❩➪❴❮❽➾❹❒❩➪❲❰✴❒↔Ï ñ❊Û✤Þ❩Ñ✱Ö❡Û✥Ö❡á✸Õ➎Ö ð ➾④➚❁ï❴❒♠➪ á✸Õ✔à☛Ö❡á❩Û❖ì❹Ñ✔Ù✙Ù✖Ñ➎Ý❞×✙Þ❩ò➐Ô❩Ò❡Ñ✔Ô✠Û✪Ò❴Ö❴×✙Û✂à✂ó ô ð ×❜à✒Ø✚Ñ✴Þ✴Ö❡×✖Þ☎Ó❩Ñ✴Ó✸à✂ë ô ð ×❜à✒à✶ã☎Ü▲Ü▲Û✚Ö❡Ò❴×❜Ø✢Û é ò é ð ➾❹➚✞ï✶❒❩➪✿➶ ð ➾❹❒↔ï✶➚↔➪ ë ô ð ➾④➚❁ï❴❒♠➪❞õ❇æ ì❹Ñ✔Ò✒Õ✔Ù✖Ù ➚✞ï✶❒✬ö❊➾✁æ❩ï✂è✌➪ ë ô ð ×❜à✒Õ➐Ô❩×✖Û✌Ø✚Û✂Ý❞×✙à❴Û❖Ù✖×✙Þ❩Û✂Õ✔Ò❪ì❹Ó❩Þ✸Ø✚Ö❴×✙Ñ✔Þ✉Ñ✱ì ➚ ì❹Ñ✔Ò❪÷❩ø♠Û✌â ❒ Õ✱Þ✸âsù☎×✙Ø✪Û✤ù✔Û✪Ò❙à❡Õ é êá❩Û✤Ô✸Õ✔Ò✶Ö❡×✙Ø✪Ó❩Ù❜Õ✱Ò❪ì❹Ñ✔Ò❡ÜúÑ✔ì②Û✪ø♠Ô❩Ò❴Û✌à❴à❴×✙Þ❩ò➐Ö❴á❩Û❦à❴Ñ✔Ù✙Ó♠Ö❴×✙Ñ✔Þ❁ë❩×✖Þ✉Ö❡Û✪Ò❡Üäà❞Ñ✱ì②Ö❴á❩Û➐û✢Ò❴Û✂Û✪Þsì❹Ó❩Þ✸Ø✽Ö❡×✖Ñ✴Þ✗ë Ý❞×✙Ù✖Ù✗Ú✠Û✤Ò❡Û✪ù☎×✙à❴×✖Ö❴Û✂âsÝ❞á❩Û✂ÞsÝ☛Û❦Õ✔â❩â❩Ò❴Û✌à❴à➏Ö❴á✸Û❖Ö❴Ñ✔Ô✸×✙Ø❖Ñ✔ì✞×✙Þ✴Ö❡Û✪ò✴Ò❡Õ✔Ù✠Û✌ü➔Ó✸Õ➎Ö❡×✖Ñ✴Þ✸à é ý❊þ✳ÿ✁￾✄✂ ☎✝✆✟✞✡✠✴ÿ☞☛✍✌✏✎✑✞✓✒ ✔Ñ✔Þ❚à✶×❜â♠Û✪Ò☛Õ✱ÞäÛ✂Ù✙Õ✴à❲Ö❡×✙Ø★Ú✸Õ✱Ò➏Ñ✱ì✗Ó❩Þ❩×✖Ö➏Ù✙Û✪Þ✸ò✱Ö❴á❆Ý❞á❩×✙Ø❙á❆×✙à✿÷❩ø♠Û✂â➨Õ✱Ö➏Ú✠Ñ✱Ö❡á➨Û✪Þ✸â✸à➏Õ✔Þ✸â➨à❴Ó❩Ú✡✕❲Û✂Ø✚Ö❴Û✌â Ö❴ÑäÕ✎Ö❡Õ✔Þ❩ò✔Û✂Þ➔Ö❴×❜Õ✱Ù✳Ù✙Ñ✴Õ✔âsÔ✠Û✪Ò✒Ó❩Þ✸×åÖ✒Ù✙Û✪Þ❩ò✔Ö❴á✗✖➾④➚✠➪✽é ✘