The order of the differential equation, whose general solution is $y=C_1 e^x+C_2 e^{2 x}+C_3 e^{3 x}+C_4 e^{x+c_5}$, where $C_1, C_2, C_3, C_4, C_5$ are arbitrary constants, is :

4

$y=\left(c_1+c_4\right) e^x+c_2 e^{2 x}+c_3 e^{3 x}+c_4 e^{c_5}$

$y=c_1 e^x+c_2 e^{2 x}+c_3 e^{3 x}+c_4 e^{c_5}$

$y=k_1 e^x+k_2 e^{2 x}+k_3 e^{3 x}+k_4$

Therefore 4 arbitrary constants

Hence (2) is the correct answer.