The order of the differential equation, whose general solution is given by…
The order of the differential equation, whose general solution is given by
$y=\left(\mathrm{c}_1+\mathrm{c}_2\right) \cos \left(x+\mathrm{c}_3\right)-\mathrm{c}_4 \mathrm{e}^{x+\mathrm{c}^5}$
where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constant, is
5
3
4
2
Solution
$\begin{aligned}
y= & \left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 \mathrm{e}^{x+c^5} \\
= & \left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 \mathrm{e}^x \mathrm{e}^{c_5} \\
= & A \cos \left(x+c_3\right)-B \mathrm{e}^x \\
\quad & \ldots\left[\mathrm{~A}=c_1+c_2, B=c_4 \mathrm{e}^{c_5}\right]
\end{aligned}$ There are 3 arbitrary constants.
$\therefore \quad$ Order of the given differential equation is 3.