A first-order linear differential equation is an equation of the form $$y' + P(t)y = Q(t)$$ where $$y'$$ is the derivative of the function $$y$$ with respect to the variable $$t$$, and $$P(t)$$ and $$Q(t)$$ are continuous functions of $$t$$. This type of equation is characterized by having a degree of one and is linear in terms of the unknown function and its derivatives. The solutions can be found using an integrating factor, which simplifies the equation into a form that can be easily solved.
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