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The order of the differential equation \( y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \) is
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Verified Answer
The correct answer is:
\( 1 \)
\( (\mathrm{C}) \)
\[
\begin{array}{l}
y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \\
=\left(c_{1} e^{c_{2}}+c_{3} e^{c_{4}}\right) e^{x} \\
=A e^{x} \\
\frac{d y}{d x}-A e^{x}=y \\
\Rightarrow \text { order }=1
\end{array}
\]
\[
\begin{array}{l}
y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \\
=\left(c_{1} e^{c_{2}}+c_{3} e^{c_{4}}\right) e^{x} \\
=A e^{x} \\
\frac{d y}{d x}-A e^{x}=y \\
\Rightarrow \text { order }=1
\end{array}
\]
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