Which of the following is a linear differential equation?

Solution

1. A first-order linear differential equation must follow the standard form $\frac{dy}{dx}+P(x)y=Q(x)$, where $P$ and $Q$ are functions of $x$.
2. Option A is non-linear due to the $y^2$ term, while options C and Dare non-linear because they involve products of $y$ and $\frac{dy}{dx}$.
3. Option B, $\frac{dy}{dx}+y=x$, satisfies the linear form with $P(x)=1$ and $Q(x)=x$.
4. Hence the answer is (B).