Question
The solution of the equation $\frac{d y}{d x}=e^{x-y}$ is :
✓
Answer
$\frac{d y}{d x}=e^{x-y}$
$=e^x \times e^{-y}$
$\Rightarrow \frac{d y}{e^{-y}}=e^x d x$
$\Rightarrow e^y d y=e^x d x$
So $\int e^y d y=\int e^x d x$
$\Rightarrow e^y=e^x+c$
$=e^x \times e^{-y}$
$\Rightarrow \frac{d y}{e^{-y}}=e^x d x$
$\Rightarrow e^y d y=e^x d x$
So $\int e^y d y=\int e^x d x$
$\Rightarrow e^y=e^x+c$
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