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SSC Pure Mathematics QUESTION #11187
Question 1
Which of the following homogeneous differential equations is NOT exact?
  • $2xy\,dx + (1+x^2)\,dy = 0$
  • $y\,dx - x\,dy = 0$✔️
  • $2+ye^{xy}\,dx + xe^{xy}\,dy = 0$ (implied form)
  • $(x+\sin y)\,dx + (x\cos y - 2y)\,dy$
Correct Answer Explanation
For $y\,dx - x\,dy = 0$: $M = y$, $N = -x$. Check: $\partial M/\partial y = 1$, $\partial N/\partial x = -1$. Since $1 \neq -1$, this is NOT exact. For option (A): $M=2xy$, $N=1+x^2$; $M_y = 2x = N_x$ — exact.