1. The problem asks: Which of the following represents the general standard form of a first-order linear differential equation? 2. The general standard form of a first-order linear differential equation is: $$y' + P(x)y = Q(x)$$ where $y'$ is the first derivative of $y$ with respect to $x$, $P(x)$ and $Q(x)$ are functions of $x$. 3. Explanation: - The equation must be linear in $y$ and its first derivative. - The term involving $y$ is multiplied by a function $P(x)$. - The right side is a function $Q(x)$. 4. Checking the options: - A: $y' + P(x)y = Q(x)$ matches the standard form. - B: $y' + P(x)y^2 = Q(x)$ is nonlinear due to $y^2$. - C: $y' + P(x)y' + Q(x)y = R(x)$ has $y'$ terms on both sides, not standard. - D: $y' = f(x,y)$ is a general form, not necessarily linear. 5. Therefore, the correct answer is option A. Final answer: A. $y' + P(x)y = Q(x)$