+C=0, B+√B2 Then, the equation becomes 0n=P(,7,中,中c,n) An alternative form can be obtained by setting X=S+n,Y=s-n pxx-pyy=F"(X,Y,,φx,φy) PARABOLIC case(B2-4AC=0) Here, we can only set a(or c) to zero(not both), other wise s and n are not independent. If we set a=0, then It can be verified, by direct evaluation, that in this case b=0, in which case we can pick n to be any function such that [J#0, and the equation becomes dm=F(s,m,,吹,) ELLIPTIC case(B2-4AC<0 This case is identical to the hyperbolic case but now s and n are complex conjugates(B4-4AC <0). Take X=S+n, y=i(s-n) and the equation F(X,Y,,中x,y Application +U. Vu=nvu+f❩❭❬✄❪❴❫❪❴❵✮❛✲❜✽❝✠❞ ❬✙❪✗❫❪❴❵✮❛❡❝✜❢❤❣❥✐✍❦ ❩❭❬✙❧♠❫ ❧♠❵✮❛✄❜❅❝✜❞ ❬✙❧♥❫ ❧♠❵✮❛❡❝✜❢✧❣❨✐✍❦ ❪✗❫ ❣♣♦❞✥❝rq❞ ❜ ♦ts❩ ✉❩ ❢ ❪❵ ❦ ❧♥❫ ❣✈♦ ❞✇❝rq❞ ❜ ♦ts❩ ✉❩ ❢ ❧❵ ❦ ①③②✍④✣⑤✮⑥✹⑦✓②✴④✬④❍⑧⑩⑨✍❶✺⑦✿❷❹❸♠⑤❻❺✙④❀❼✗❸♥❽✘④❀❾ ❿☞➀✖➁ ❣❨➂✬➃➅➄ ❪ ❦ ❧ ❦ ❿ ❦ ❿☞➀ ❦ ❿✙➁✺➆✗➇ ➈⑤●❶♠➉➊⑦✓④✣➋✓⑤✍❶➌⑦✓❷➎➍♥④➐➏➑❸♥➋✿❽➒❼❍❶✺⑤❭❺☞④✬❸♠❺✹⑦✖❶✺❷❹⑤✴④❍➓➔❺➣→❉❾✦④✣⑦✦⑦✓❷➎⑤✴↔❡↕ ❣ ❪ ❝ ❧ ⑥❭➙ ❣ ❪ ♦ ❧✄➛ ❿☞➜✽➜ ♦ ❿✄➝➞➝ ❣✇➂➃ ➃ ➄↕ ❦ ➙ ❦ ❿ ❦ ❿☞➜ ❦ ❿✄➝✽➆ ➟➈➐➠➐➈➐➡❯➢❲➤✮➥✿➦ ❼✣❶♠❾✿④ ➄➧❞❜ ♦➨s❩❢✧❣❥✐ ➆ ➛ ➩❯④❍➋✿④♥⑥✱➫✽④❉❼❍❶✺⑤➭❸♠⑤✍➉➎→➯❾✦④✣⑦✘➲ ➄❸♥➋✒➳➆ ⑦✓❸➸➵✣④❍➋✿❸ ➄⑤✴❸✺⑦✘❺✙❸♠⑦✿②➆ ⑥➺❸✺⑦✓②✴④✣➋✓➫❖❷❹❾✿④ ❪ ❶♠⑤✍➓ ❧ ❶✺➋✓④❡⑤✴❸✺⑦ ❷❹⑤✍➓✹④✣➻☞④✣⑤✙➓✹④✣⑤⑩⑦ ➇ ➥➏➺➫✽④✬❾✦④✣⑦❖➲ ❣❨✐ ⑥➣⑦✿②✴④❍⑤ ❪❴❫ ❪❵ ❣ ♦ ✉ ❞ ❩➽➼ ➥⑦✽❼❍❶✺⑤❊❺☞④❲➍♠④✣➋✓❷➎➾✍④❍➓✲⑥♥❺➣→➚➓✴❷➎➋✓④❍❼✗⑦❅④✣➍➌❶♠➉➎⑨✍❶✺⑦✿❷❹❸♠⑤✮⑥♥⑦✿②✙❶➌⑦③❷➎⑤❡⑦✓②✴❷➪❾✽❼❍❶♠❾✿④✁➶ ❣❥✐ ⑥⑩❷❹⑤❊➫❖②✴❷➪❼✖②❉❼❍❶♠❾✿④❯➫❅④ ❼✣❶♠⑤➔➻✍❷❹❼✖➹ ❧ ⑦✿❸❡❺☞④❉➘➌➴✙➷➐➏➑⑨✴⑤✙❼❴⑦✿❷❹❸♠⑤●❾✿⑨✍❼✖②➔⑦✿②✍❶✺⑦✶➬➱➮✷➬☞✃❣✇✐ ⑥✴❶♠⑤✍➓❊⑦✓②✴④✬④❍⑧⑩⑨✍❶✺⑦✿❷❹❸♠⑤❻❺✙④❀❼✗❸♥❽✘④❀❾ ➛ ❿➁✗➁ ❣❨➂➃ ➄ ❪ ❦ ❧ ❦ ❿ ❦ ❿➀ ❦ ❿➁ ➆ ➼ ❐➤✱➤✮➥➟❅①➥✿➦ ❼✣❶♥❾✦④ ➄➧❞❜ ♦ts❩❢✩❒❮✐ ➆ ➛ ①③②✴❷➪❾❭❼✣❶♠❾✿④❰❷➪❾❻❷❹➓✴④✣⑤⑩⑦✿❷➪❼✣❶♠➉✁⑦✓❸✜⑦✓②✴④➯②➣→⑩➻☞④✣➋✓❺☞❸♠➉❹❷❹❼t❼✣❶♥❾✦④➨❺✴⑨✹⑦●⑤✴❸➌➫ ❪ ❶✺⑤✍➓ ❧ ❶✺➋✓④➨❼✣❸♠❽➚➻✴➉❹④✗Ï ❼✗❸♥⑤➌Ð❂⑨✴↔⑩❶➌⑦✿④❀❾ ➄➧❞❜ ♦➯s❩❢Ñ❒✥✐ ➆❴➇ ①Ò❶✺➹♥④Ó↕ ❣ ❪ ❝ ❧ ⑥➯➙ ❣☎Ô❴➄ ❪ ♦ ❧ ➆ ❶✺⑤✍➓●⑦✿②✴④✶④❍⑧⑩⑨✍❶➌⑦✓❷➎❸♥⑤ ❺☞④❍❼✗❸♥❽➚④❍❾ ➛ ❿➜③➜ ❝ ❿➝➞➝ ❣❨➂➃ ➄↕ ❦ ➙ ❦ ❿ ❦ ❿➜ ❦ ❿➝ ➆✗➇ Õ☞Ö➧Õ☞Ö➧Õ ×❉Ø✱Ø➞Ù➧ÚÜÛ♠Ý✹Þ❀Ú➧ß☞à✱á â☞ã⑩äæåèçté ê☞ë ê☞ì ❝ríïî❀ð ë ❣✇ñ☞ð❜ ë ❝✕ò ó✗ô ë ❷➪❾ ➼❍➼✣➼ õ