Explanation

(c)
Given, $y = c_{1}\cos{(x + c_{2})} + c_{3}\sin{(x + c_{4})} + c_{5}e^{x} + c_{6}$
$y = c_{1}\left\lbrack \cos x\cos c_{2} - \sin x\sin c_{2} \right\rbrack$
$+ c_{3}\lbrack\sin{x\cos{c_{4} + \cos{x\sin c_{4}}}\ }\rbrack + c_{5}e^{x} + c_{6}$
$= \cos x\left( c_{1}\cos c_{2} + c_{3}\sin c_{4} \right) + \sin x\left( - c_{1}\sin c_{2} + c_{3}\cos c_{4} \right) + c_{5}e^{x} + c_{6}$
$= A\cos x + B\sin x + Ce^{x} + D$
Where $A = c_{1}\cos c_{2} + c_{3}\sin c_{4}$
$B = - c_{1}\sin c_{2} + c_{3}\cos c_{4},\ \ C = c_{5},\ D = c_{6}$
Hence, order is 4.