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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