First Order Differential Problem

[gpax42]

Homework Statement

Show that if a and $$\lambda$$ are positive constants, and b is any real number, then every solution of the equation dx/dt + ax = b*exp(-$$\lambda$$*t) has the property that x(t) --> 0 as t --> $$\infty$$

The Attempt at a Solution

i tried considering the cases where a = $$\lambda$$ and a $$\neq$$ $$\lambda$$ but kept getting stuck... any suggestions?

 

[rock.freak667]

Try solving

$$\frac{dx}{dt}+ax=be^{- \lambda t}$$

by multiplying by an integrating factor.