[數學]一個工數的問題~有請會的人多多指導小弟一下~~感激不儘唷!
由 refa 於 星期六 三月 11, 2006 2:32 pm
#ed_op#DIV#ed_cl##ed_op#DIV#ed_cl# y'=y * (x-1)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#/y+3#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#之通解為#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# y + 3ln|y| = 1/3(x-1)#ed_op#SUP#ed_cl#3#ed_op#/SUP#ed_cl#+k ...........(1.3)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#欲滿足y(3)=1,令x= 3 且 y= -1代入方程式(1.3)得#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# -1 = 1/3(2)#ed_op#SUP#ed_cl#3 #ed_op#/SUP#ed_cl#+ k ,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#故 k = -11/3#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#此初值問題之解為#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# y + 3ln|y| = 1/3(x-1)#ed_op#SUP#ed_cl#3#ed_op#/SUP#ed_cl# -11/3#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#而我的問題是為什麼要滿足y(3)=1 , 令 x=3 且 y= -1呀!#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#還是有更好的解法呢?~#ed_op#/DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#