The solution of the equation d y d x =e^ x-y is :

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.

$e^y=e^x+c$

$\frac{d y}{d x}=e^{x-y}=e^x \times e^{-y}$
$\Rightarrow \frac{d y}{e^{-y}}=e^x d x$
$\Rightarrow e^y d y=e^x d x$
$\text { So } \int e^y d y=\int e^x d x$
$\Rightarrow e^y=e^x+c$
Hence the correct choice is $(C).$

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