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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The general solution of the differential equation $x d y+y d x=0$ is:
  • ✓
    $x y=c$
  • B
    $x+y=c$
  • C
    $x^2+y^2=c^2$
  • D
    $\log y=\log x+c$
✓

Answer

Correct option: A.
$x y=c$
We have, $x d y+y d x=0$
$\Rightarrow x d y=-y d x $
$\Rightarrow \int \frac{d y}{y}=-\int \frac{d x}{x} $
$\Rightarrow \log y=-\log x+\log c $
$\Rightarrow y=\frac{c}{x}$
$\Rightarrow x y=\text { constant }$

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