x=(1/2)exp(t) is a particular integral of dx/dt+x=exp(t), as can be

seen by differentiating it and substituting it and its derivative into

the equation.

The general solution is a particular integral plus a solution to the

homogeneous equation dx/dt+x=0. Which is Aexp(-t).

So the general solution is: x(t)=Aexp(-t)+(1/2)exp(t).

RonL