First order linear differential equations

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Given a FOLDE

$y'=ay+b$

$a, b$ costants

• Homogeneous

$y(t)=Ae^{-at}$ General solution of the homogeneous

• Non-homogeneous

$y_p=- \frac{b}{a}$

$y_c=Ae^{-at}$

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

• $a, b$ function