y'+2y=e^x怎么解满足初始条件y(0)=1/3

y'+2y=e^x怎么解满足初始条件y(0)=1/3
y'+2y=e^x怎么解
满足初始条件y(0)=1/3

y'+2y=e^x怎么解满足初始条件y(0)=1/3
其特征方程：r+2=0
r=-2
其齐次通解为y=Ce^(-2x)
设其特解是y=ae^x
代入原方程得a=1/3,y=1/3e^x
所以其通解是y=Ce^(-2x)+1/3e^x
y(0)=1/3,代入得,C＝0
因此特解是y=1/3e^x