Re: [分析] 常微分方程式一題
1
I = -----------
M^2 + N^2
滿足 A = B 即是正合...
d d I d M
令 A = --- (IM) = --- * M + I * ---
d y d y d y
-2 (MMy+NNy) 1
= -------------- * M + ----------- * My
(M^2 + N^2)^2 M^2 + N^2
1
=---------------- * { M^2 * My + N^2 * My - 2M^2 * My - 2MN * Ny }
( M^2 + N^2 )^2
(再把上式代入條件: Ny = Mx ; My = - Nx )
1
=---------------- * { -M^2 * Nx - N^2 * Nx + 2M^2 * Nx - 2MN * Mx }
( M^2 + N^2 )^2
1
=---------------- * { M^2 * Nx - N^2 * Nx - 2MN * Mx }
( M^2 + N^2 )^2
同理
d d I d N
再令 B = --- (IN) = --- * N + I * ---
d x d x d x
-2 (MMx+NNx) 1
= -------------- * N + ----------- * Nx
(M^2 + N^2)^2 M^2 + N^2
1
=---------------- * { M^2 * Nx + N^2 * Nx - 2MN * Mx - 2N^2 * Nx }
( M^2 + N^2 )^2
1
=---------------- * { M^2 * Nx - N^2 * Nx - 2MN * Mx }
( M^2 + N^2 )^2
....A = B
囧 怎會這樣?
那如果不這樣算 該怎麼算呢
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08/14 06:14, , 1F
08/14 06:14, 1F
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