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 ____

Answer 1

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 $3 .$