GATE 2025 Chemical Engineering, Q44 · Mathematics
The correct answers are B. y = c/x; c is a constant; D. y = 0.
Question
Consider the differential equation dy/dx + y/x = 0. Choose the CORRECT option(s) for the solution y.
Official answer: B. y = c/x; c is a constant; D. y = 0
Why
GATE 2025 official key: (B, D). Separating variables, dy/y = −dx/x ln y = −ln x + const y = c/x, which includes the trivial solution y = 0 as the c = 0 case.
Explanation cross-checked for consistency. Final answer matches the official IIT answer key.