1. The problem asks: Which of the following represents the general standard form of a first-order linear differential equation? 2. The standard form of a first-order linear differential equation is given by: $$y' + P(x)y = Q(x)$$ where $y'$ is the first derivative of $y$ with respect to $x$, $P(x)$ and $Q(x)$ are functions of $x$ only. 3. Explanation: - The equation must be first order, so it involves $y'$ but not higher derivatives. - It must be linear in $y$ and $y'$, so powers of $y$ or $y'$ other than 1 are not allowed. - $P(x)$ and $Q(x)$ can be any functions of $x$. 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: $y'' + P(x)y' + Q(x)y = R(x)$ is second order (involves $y''$). - D: $y' = f(x,y)$ is not necessarily linear or in standard form. 5. Therefore, the correct answer is option A. Final answer: A. $y' + P(x)y = Q(x)$