Re: [工數] ODE求解
※ 引述《xuptjo (風)》之銘言：
: 幫學弟解題 但自己不會 Q_Q
: y``-3y`+2y=cos(e^-x)
: yh會算
: 但yp不會算!!!
: 求解 附上小小200P 感謝
Variation of parameters
Known that yc=c1 Exp[x]+ c2 Exp[2x]
W = | Exp[x] Exp[2x] | =Exp[3x]
| Exp[x] Exp[2x]2|
u1'= Exp[-3x] | 0 Exp[2x]| =-Exp[-x]Cos[Exp[-x]]
|Cos[Exp[-x]] 2Exp[2x]|
u2'= Exp[-3x] | Exp[x] 0|=Exp[-2x]Cos[Exp[-x]]
| Exp[x] Cos[Exp[-x]] |
Integrate them with sustitution u=Exp[-x]
u1=Sin[Exp[-x]] u2=-Exp[-x]Sin[Exp[-x]]+Cos[Exp[-x]]
yp= yc1 u1 + yc2 u2= Exp[2x]Cos[Exp[-x]]
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