Question

The order of the differential equation associated with the primitive $y=c_{1}+c_{2} e^{x}+c_{3} e^{-2 x+c_{4}}$, where $c_{1}, c_{2}, c_{3}, c_{4}$ are arbitrary constants, is

• A. 3
• B. 4
• C. 2
• D. None of these

Answer 1

Answer: (A)

We have $y=c_{1}+c_{2} e^{x}+c_{3} e^{-2 x+c_{4}}$
$\Rightarrow y=c_{1}+c_{2} e^{x}+c_{3} e^{-2 x} \cdot e^{c_{4}}$
$\Rightarrow y=c_{1}+c_{2} e^{x}+c_{3}' e^{-2 x},$
where $c_{3}'=c_{3} e^{c_{4}}$
It is an equation containing three arbitrary constants.
So, the associated differential equation is of order $3$.