The order of the differential equation, whose solution is $y=\left(C_1+C_2\right) \mathrm{e}^x+C_3…
The order of the differential equation, whose solution is $y=\left(C_1+C_2\right) \mathrm{e}^x+C_3 \mathrm{e}^{x+C_4}$, is
- 4
- 1
- 3
- 2
Solution
$\begin{aligned}
y & =\left(C_1+C_2\right) \mathrm{e}^x+\mathrm{C}_3 \mathrm{e}^{x+\mathrm{C}_4} \\
& =\mathrm{Ae}^x+\mathrm{Be}^x \text {, where } \mathrm{A}=\mathrm{C}_1+\mathrm{C}_2 \text { and } \mathrm{B}=\mathrm{C}_3 \mathrm{e}^{\mathrm{C}_4} \\
& =(\mathrm{A}+\mathrm{B}) \mathrm{e}^x \\
& =\mathrm{De}^x, \text { where } \mathrm{D}=\mathrm{A}+\mathrm{B}
\end{aligned}$
This equation consist of one arbitrary constant.
Asked in: MHT CET 2024 (15 May Shift 2)
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