First order linear differential equations

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Given a FOLDE

$$ y'=ay+b$$

$$a, b$$ costants
$$y(t)=Ae^{-at} $$             General solution of the homogeneous
 * Homogeneous

$$y_p=- \frac{b}{a}$$
 * Non-homogeneous

$$y_c=Ae^{-at} $$

$$y(t)=Ae^{-at}- \frac{b}{a} $$     General solution of the non-homogeneous


 * $$a, b$$ function