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MODEL PAPER 2025 — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMODEL PAPER 20251 Mark
MCQ
What is the general solution of the differential equation $e ^{ y ^{\prime}}= x ?$
  • A
    $y=x \log x+c$
  • ✓
    $y=x \log x-x+c$
  • C
    $y=x \log x+x+c$
  • D
    $y=x+c$
✓

Answer

Correct option: B.
$y=x \log x-x+c$
The given differential equation $e^{y^{\prime}}=x$
$\Rightarrow \frac{d y}{d x}=\log x$
$ d y=\log x d x$
$\Rightarrow\int d y=\int \log x d x$
$y=x \log x-x+c$
hence the correct option is $(B).$

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