Question

求下列微分方程满足初始条件的特解

求下列微分方程满足初始条件的特解微积分

Answer 1

y(0) =1
y'(0)=2
y''-3y'+2y =5
The aux.equation
p^2-3p+2p=0
(p-2)(p-1)=0
p=1 or 2
let
y= Ae^x+Be^(2x) + C
2C=5
C= 5/2
y(0)= A+B+5/2 =1 (1)
y'=Ae^x+2Be^(2x)
y'(0) = A+2B =2 (2)
(2)-(1)
B- 5/2 = 1
B= 7/2
from (2)
A+2B =2
A+7=2
A=-5
ie
y= -5e^x+(7/2)e^(2x) + 5/2