Rewrite in standard linear form: $\frac{dy}{dx} + \frac{y}{x\log x} = 2$

Integrating factor: $e^{\int \frac{1}{x\log x}dx} = e^{\ln(\log x)} = \log x$

Multiply through: $\frac{d}{dx}(y \log x) = 2\log x$

Integrate: $y\log x = 2(x\log x - x) + C$

At $x=1$: $y(1)\cdot 0 = 2(0-1)+C \Rightarrow C=2$

So $y\log x = 2x\log x - 2x + 2$. At $x=e$: $y(1) = 2e - 2e + 2 = \mathbf{2}$

The key signal here is the word strange/puzzling at the start — this sets up a contrast. If her writing is commonly thought to be tortuous (meaning twisting, overly complex, hard to follow), then the blank must introduce a word that contradicts that reputation.

• Painstaking — means thorough and careful; does not contradict the notion of being tortuous.
• Tedious — means boring and slow; actually reinforces the idea of difficult writing.
• Insightful — means perceptive; does not directly contrast with being hard to follow.
• Clear — directly contradicts the notion of tortuous (convoluted) writing. If her essays are extremely clear, it is indeed strange that she has a reputation for complexity.

Correct Answer: D — Clear. The sentence uses “although” to signal contrast, and the framing word “strange” confirms we need the opposite of tortuous.