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{\bf Question}

Find the general solution of the differential equation
$\displaystyle \frac{dx}{dt} = e^{(x - t)}$

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{\bf Answer}

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$\displaystyle \frac{dx}{dt} = e^{(x - t)}$
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Separable:
\begin{eqnarray*} \frac{dy}{dx} & = & e^xe^{-t} \\ \Rightarrow
e^{-t} \, dt & = & e^{-x} \, dx \\ \int e^{-t} \, dt & = & \int
e^{-x} \, dx \\ \Rightarrow -e^{-t} & = & -e^{-x} +
\mathrm{constant} \\  \Rightarrow e^{-t} & = & e^{-x} +
\mathrm{constant}
\\
\end{eqnarray*}



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