[微積] 微分方程逆運算法和一題積分
1.
1 D+1
------- (-2sinx) = ----------- (-2sinx) <= 這個等式看不懂
D^3 +1 (-D+1)(D+1)
= -cosx -sinx
2.書上寫
π/w
w∫ sin wx cos nwx dx = (1+cosnπ)/(1-n^2) (n≠1)
0
π/w π/w
我算 w∫ sin wx cos nwx dx = w(1/2)∫ sin(n+1)wx -sin(n-1)wx dx
0 0
π/w
= (1/2) [-cos(n+1)wx/(n+1) +cos(n-1)wx/(n-1)]
0
= (1/2) [cos(n-1)π/(n-1) - cos(n+1)π/(n+1)]
= (-1)^(n+1) / (n^2 -1) (n≠1)
我檢查了這個答案和書上寫的應該是不一樣的 請問是哪裡不對嗎 謝謝
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