Chemegate

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.

  • A. y = x + c; c is a constant
  • B. y = c/x; c is a constant
  • C. y = −x + c; c is a constant
  • D. y = 0

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 \Rightarrow ln y = −ln x + const \Rightarrow 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.