[理工] [工數]-台大92-C卷
請問第二題和第三題怎麼解?
2.can we express the general solution of the following differential equation
in a power series? Why?
Find the general solution
(x^4)(d^2y/dx^2)+(2x^3)(dy/dx)+y=0
3.
(D-2)x-y-6z=0
(D-2)y-(2D+1)z=0
(D-2)x-y+(D-8)z=0
(a)find general solution
(b)suppose x(0)=y(0)=z(0)=0 find the 拉普拉斯轉換 of x,y,z
我解出來是 x=(e^2t)[(5/2)C3t^2+(C2+6C3)t+C1]
y=(e^2t)[(5)C3t+C2]
z=(e^2t)[C3]
可是帶入x(0)=y(0)=z(0)=0的條件，會得到C1=C2=C3=0........好奇怪
不知道哪裡算錯?
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