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Model Paper 6 — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsModel Paper 61 Mark
MCQ
The general solution of the differential equation $\frac{d y}{d x}=\frac{y}{x}$ is
  • ✓
    $y = kx$
  • B
    $\log(y) - kx$
  • C
    $\cos x$
  • D
    $\tan x$
✓

Answer

Correct option: A.
$y = kx$
We have,
$\frac{d y}{d x}=\frac{y}{x}$
$\Rightarrow \frac{d y}{y}=\frac{d x}{x}$
Integrating on both sides,
$\int \frac{d y}{y}=\int \frac{d x}{x}$
$\log |y|=\log |x|+\log k$
$\Rightarrow \log \left(\frac{y}{x}\right)=\log k$
$\Rightarrow y = kx$

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