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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
Solution of the differential equation $\frac{{dx}}{x} + \frac{{dy}}{y} = 0$ is
  • ✓
    $xy = c$
  • B
    $x + y = c$
  • C
    $\log x\,\,\log y = c$
  • D
    ${x^2} + {y^2} = c$
✓

Answer

Correct option: A.
$xy = c$
a
(a) Differential equation $\frac{{dx}}{x} + \frac{{dy}}{y} = 0$. Integrating, we get $\int {\frac{{dx}}{x} + \int {\frac{{dy}}{y} = 0} } $ or $\log x + \log y = \log c$

or $\log (xy) = \log c$ or $xy = c$.

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