How to solve a simple differential equations?

Question

I have a problem about differential equations.

$\dot{x}(t) = - \lambda x(t)+b$

How to solve this equations?

Thanks a lot!

Answer 1

Hint

The easiest way could be to define $$x(t)=y(t)+\frac b\lambda \implies x'(t)=y't)\implies y'(t)=-\lambda y(t)$$ which looks very simple.

Answer 2

Separate variables:

$\frac{dx}{-\lambda x + b} = dt$

And integrate both sides.