作者lookyya (死神~露琪亞)
看板Grad-ProbAsk
標題Re: [理工] [工數]-ODE
時間Tue Oct 27 12:10:58 2009
※ 引述《JaLunPa (呷懶趴)》之銘言：
: 1. (D^4 +5D^2 -36)y=10e^-2x +3cox3x
4 2 2 2
m +5m -36 =(m +9)(m -4)=0 m=+3i,-3i,+2,-2
yc= C1*Cos3x + C2*Sin3x + C3*exp(2x) + C4*exp(-2x)
yp1= A*x*exp(-2x)
yp2=B*x*Cos3X + C*x*Sin3x
針對yp2的話
yp2' = (3C)*x*Cos3x+(B)*Cos3x+(-3B)*x*Sin3x+(C)*Sin3x
yp2" = (-9B)*x*Cos3x+(6C)*Cos3x+(-9C)*x*Sin3x+(-6B)*Sin3x
yp2"'= (-27C)*x*Cos3x+(-27B)*Cos3x+(27B)*x*Sin3x+(-27C)*Sin3x
yp2""= (81B)*x*Cos3x+(-108C)*Cos3x+(81C)*x*Sin3x+(108B)*Sin3x
108B -30B =0
30C -108C =3
-78C = 3
B=0 C = -1/26
yp2= C*x*Sin3x = (-1/26)*sin3X
你應該只是計算錯誤~
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1F：推 JaLunPa:謝謝 10/27 14:31
2F：推 JaLunPa:呵呵 我都習慣用逆運算子 待定係數很怕式子太多錯 10/27 15:28