常微分方程第三版答案2.1

1、常微分方程習題2.11.,并求滿足初始條件：x=0,y=1的特解. 解：對原式進行變量分離得 并求滿足初始條件：x=0,y=1的特解.解：對原式進行變量分離得：3 解：原式可化為： 12解1516解： ，這是齊次方程，令17. 解：原方程化為 令方程組則有令當當另外 19. 已知f(x).解：設f(x)=y, 則原方程化為 兩邊求導得20.求具有性質 x(t+s)=的函數(shù)x(t),已知x(0)存在。解：令t=s=0 x(0)= 若x(0)0 得x=-1矛盾。所以x(0)=0. x(t)=) 兩邊積分得arctg x(t)=x(0)t+c 所以x(t)=tgx(0)t+c 當t=0時 x(0)=

2、0 故c=0 所以x(t)=tgx(0)t02411 黃罕鱗（41） 甘代祥（42）acknowledgements my deepest gratitude goes first and foremost to professor aaa , my supervisor, for her constant encouragement and guidance. she has walked me through all the stages of the writing of this thesis. without her consistent and illuminating instr

3、uction, this thesis could not havereached its present form. second, i would like to express my heartfelt gratitude to professor aaa, who led me into the world of translation. i am also greatly indebted to the professors and teachers at the department of english: professor dddd, professor ssss, who h

4、ave instructed and helped me a lot in the past two years. last my thanks would go to my beloved family for their loving considerations and great confidence in me all through these years. i also owe my sincere gratitude to my friends and my fellow classmates who gave me their help and time in listeni

5、ng to me and helping me work out my problems during the difficult course of the thesis. my deepest gratitude goes first and foremost to professor aaa , my supervisor, for her constant encouragement and guidance. she has walked me through all the stages of the writing of this thesis. without her cons

6、istent and illuminating instruction, this thesis could not havereached its present form. second, i would like to express my heartfelt gratitude to professor aaa, who led me into the world of translation. i am also greatly indebted to the professors and teachers at the department of english: professo

7、r dddd, professor ssss, who have instructed and helped me a lot in the past two years. last my thanks would go to my beloved family for their loving considerations and great confidence in me all through these years. i also owe my sincere gratitude to my friends and my fellow classmates who gave me their h