f''(x)+f(x)=2e^x
Lian lide
f'(x)-3f(x)=-2e^x ②
F'(x)-3f(x)=0
Get ln|f(x)|=3x+C 1。
f(x)=Ce^(3x)=u(x)e^(3x)
Substitution of constant variation method into ②
u'(x)e^(3x)=-2e^x
Then u' (x) =-2e (-2x)
So u (x) = e (-2x)+c
Then f (x) = u (x) e (3x)
=(e^(-2x)+C)e^(3x)
=e^x+Ce^(3x)
Substitute (1)
C=0
So f (x) = e x