推 bat205:THANKS~ 05/04 16:24
※ 引述《bat205 (時速200km)》之銘言：
: Use the transformation z=sin(x) to solve
: d^2(y)/dx^2+tan(x)dy/dx+(cos^2(x))y=0
: 感恩^^
dy dy dz dy
令 z = sinx , 則---- = ---- ---- = cosx ----
dx dz dx dz
2 2
d y dy 2 d y
----- = -sinx ---- + cos x ----- ,代入ODE
dx^2 dz dz^2
2
dy
得 ----- + y = 0
dz^2
y = C1 cosz + C2 sinz = C1 cos(sinx) + C2 sin(sinx)
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