The order of the differential equation, whose solution is y= (C_1+C_2 ) e^x+C_3 e^x+C_4 , is

Correct answer: (B) 1. y = (C_1+C_2 ) e^x+C_3 e^x+C_4 =Ae^x+Be^x , where A=C_1+C_2 and B=C_3 e^C_4 =(A+B) e^x =De^x, where D=A+B This equation consist of one arbitrary constant.

Q60 / 150 · MHT CET 2024 (15 May Shift 2) · Mathematics

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

A
4
Correct answer
B
1
C
3
D
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.

Hence, the correct answer is option: 'B'.

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