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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The solution of the equation $\frac{d y}{d x}=e^{x-y}$ is :
  • A
    $e^x=e^{-y}+c$
  • B
    $e^y=e^{-x}+c$
  • ✓
    $e^y=e^x+c$
  • D
    $e^{-x}=e^{-y}+c$
✓

Answer

Correct option: C.
$e^y=e^x+c$
(C)
$
\begin{array}{l}
\frac{d y}{d x}=e^{x-y}=e^x \times e^{-y} \\
\Rightarrow \quad \frac{d y}{e^{-y}}=e^x d x \\
\Rightarrow \quad e^y d y=e^x d x \\
\text { So } \quad \int e^y d y=\int e^x d x \\
\Rightarrow \quad e^y=e^x+c
\end{array}
$
Hence the correct choice is (C).

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