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工程數學 題目懇請大大幫解題目
麻煩求解 1.15 1.16 2.4 (c) (d) 最後兩題求全解<div></div> 本帖最後由 chongwaikei 於 2013-1-15 12:21 AM 編輯
我不是讀工程的, 只能幫你計算數學的部份...
http://latex.codecogs.com/gif.latex?\\y%27%27+y=2\cos%20x\\\\$firstly%20we%20consider%20$y%27%27+y=0\\\\%20$let%20$y=e^{kx}\;\Rightarrow%20y%27%27=k^2e^{kx}\\\\%20\Rightarrow%20\;(k^2+1)e^{kx}=0\\\\%20\Rightarrow%20\;k=\pm%20i\\\\%20$so%20,%20$y_1=c_1e^{ix}=c_1(\cos%20x+i\sin%20x)$%20and%20$y_2=c_2e^{-ix}=c_2(\cos%20x-i\sin%20x)\\\\%20$the%20general%20solution%20of%20$y%27%27+y=0$%20is%20:%20$\\\\%20y=y_1+y_2\\\\%20=C_1\cos%20x+C_2\sin%20x
http://latex.codecogs.com/gif.latex?\\$Now%20we%20solve%20the%20particular%20solution%20of%20$y%27%27+y=2\cos%20x\\\\%20y_p=x(a\cos%20x+b\sin%20x)\\\\%20\Rightarrow%20\;y_p%27%27=-2a\sin%20x-bx\sin%20x-ax\cos%20x+2b\cos%20x\\\\%20\Rightarrow%20\\\\%20y_p%27%27+y_p=2\cos%20x\\\\-2a\sin%20x-bx\sin%20x-ax\cos%20x+2b\cos%20x+ax\cos%20x+bx\sin%20x=2\cos%20x\\\\2b\cos%20x-2a\sin%20x=2\cos%20x\\\\%20\Rightarrow%20\;a=0\;,\;b=1\\\\%20y_p=x\sin%20x\\\\%20$Since%20,%20the%20general%20solution%20of%20$y%27%27+y=2\cos%20x$%20is%20:%20$\\\\%20\boxed{y=C_1\cos%20x+C_2\sin%20x+x\sin%20x}
http://latex.codecogs.com/gif.latex?\\$same%20as%20part%20c)%20$y%27%27-y=x\sin%20x\\\\%20$you%20will%20get%20the%20general%20solution%20:%20$\\\\%20y=C_1e^x+C_2e^{-x}-\frac{x\sin%20x+\cos%20x}{2}\\\\%20$and%20$y%27=C_1e^x-C_2e^x-\frac{x\cos%20x}{2}\\\\%20y(0)=y%27(0)=0\\\\%20\Rightarrow%20\;C_1=\frac{1}{4}$%20and%20$C_2=\frac{1}{4}\\\\%20$Since%20,%20$y=\frac{e^x+e^{-x}}{4}-\frac{x\sin%20x+\cos%20x}{2}\\\\%20$or%20$y=\frac{\cosh%20x-x\sin%20x+\cos%20x}{2}
...<div class='locked'><em>瀏覽完整內容，請先 <a href='member.php?mod=register'>註冊</a> 或 <a href='javascript:;' onclick="lsSubmit()">登入會員</a></em></div> 1.15
求Vc(0)=?
Vc(0)=60*(60+20)*40=30V
(a)t>=0+
Vc(t)+R*ic(t)=90V
Vc(t)+R*C*(dVc(t)/dt)=90
dVc(t)/dt+Vc(t)/RC=90/RC
dVc(t)/dt+5Vc(t)=450
代入一階線性公式
I(t)=e^S5dt=e^5t
Vc(t)I(t)=Se^5t*450dt=90e^5t+c
Vc(t)=90+ce^-5t
因Vc(0)=30 故90+c=-30 c=-120
Vc(t)=90-120e^-5t V t>=0+
ic(t)=c(dVc(t)/dt)=0.5*10^-6*d/dt(90-120e^-5t)
=300e^-5t uA t>=0+
1.16 明天再幫你解先ZZZ
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