[理工] [工數]-簡單ODE ~"~
dy 1
---= ------
dx x+y+1
(x+y+1)dy-dx=0
令u=x+y . y =u-x . dy=du-dx
x(du-dx)+(u-x)(du-dx)+(du-dx)-dx=0
u(du-dx)+du-2dx = 0
(u+1)du-(u+2)dx=0
(u+1)
-----du -dx = 0
(u+2)
1
---ln(u+2)^2 + ln(u+2) -x = c
2
1
---ln(x+y+2)^2 + ln(x+y+2) -x = c
2
這樣算對嗎?
u
----du 積分 有人能白話解釋 一下積分嗎?
u+2
我怕我觀念錯了..
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