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!

$\frac{dx(t)}{dt} = - \lambda x(t)+b$
`$\frac{dx(t)}{ x(t) } = - \lambda dt +\frac{b dt}{x(t)}$' — Carl, Sep 26 '17 at 04:15

score 1 · Answer 1 · answered Sep 26 '17 at 04:12

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.

answered Sep 26 '17 at 04:12

Claude Leibovici

score 0 · Answer 2 · answered Sep 26 '17 at 04:17

0

Separate variables:

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

And integrate both sides.

answered Sep 26 '17 at 04:17

L. Ko

2 Answers2