Home › MCQs › SSC Pure Mathematics › Question #11184
Back to Questions
SSC Pure Mathematics QUESTION #11184
Question 1
The differential equation $xy'' + y' = 0$ has a solution $y = \ln x$ on the interval:
  • $(0,\infty)$✔️
  • $(-\infty,0)$
  • $(-\infty,\infty)$
  • $[0,\infty[$
Correct Answer Explanation
Substituting $y = \ln x$: $y' = 1/x$, $y'' = -1/x^2$. Then $xy'' + y' = x(-1/x^2) + 1/x = -1/x + 1/x = 0$. This is valid wherever $\ln x$ is defined: $x > 0$, i.e. the interval $(0,\infty)$.