Bihar BoardHindi Mediumकक्षा 12 साइन्सगणितअवकल समीकरण1 Mark
MCQ
समीकरण $\frac{d y}{d x}=e^{x-y}$ का हल है-
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) $e^y=e^x+c$ $\frac{d y}{d x}=e^{x-y}=e^x \times e^{-y}$ $\begin{array}{ll}\Rightarrow \frac{d y}{e^{-y}}=e^x d x \\ \Rightarrow e^y d y=e^x d x\end{array}$ इसलिए $\int e^y d y=\int e^x d x$ $\Rightarrow e^y=e^x+c$ अतः सही विकल्प (C) है।
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