求下列微分方程的特解(1)xy'+y-e^x=0,y|(x=a ) =b(2)y'-(2/x)y=(1/2)x,y|(x=1) =2

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求下列微分方程的特解(1)xy'+y-e^x=0,y|(x=a ) =b(2)y'-(2/x)y=(1/2)x,y|(x=1) =2

求下列微分方程的特解(1)xy'+y-e^x=0,y|(x=a ) =b(2)y'-(2/x)y=(1/2)x,y|(x=1) =2
求下列微分方程的特解
(1)xy'+y-e^x=0,y|(x=a ) =b
(2)y'-(2/x)y=(1/2)x,y|(x=1) =2

求下列微分方程的特解(1)xy'+y-e^x=0,y|(x=a ) =b(2)y'-(2/x)y=(1/2)x,y|(x=1) =2
(1)xy'+y-e^x=0
(xy)'=e^x,xy=e^x+C,y(a)=b,ab-e^a=C xy=e^x+ab-e^a
(2)y'-(2/x)y=(1/2)x
由通解公式:y=Cx^2+x

(1)xy'+y-e^x=0
(xy)'=e^x,->xy=e^x+C又y(a)=b,, ab-e^a=C ->xy=e^x+ab-e^a
(2)y'-(2/x)y=(1/2)x
->y=2x^2+lnx/2