y=f(x)则做Laplace变换L(y)=L(f(x))=F(s)再对y'+y=1两边做Laplace变换：L(y')+L(y)=L(1)即sF(s)-f(0)+F(s)=1/s也就是F(s)=1/s(s+1)=1/s-1/(s+1)再做Laplace逆变换f(x)=L^-1(F(s))=L^-1(1/s-1/(s+1))=1-e^(-x)
