$y=\left(a+b\right)\sin \left(x+c\right)-d{e}^{x+e+f}$

Differentiating, we get

$\frac{dy}{dx}=\left(a+b\right)\cos \left(x+c\right)-d{e}^{x+e+f}$

i.e. $\frac{dy}{dx}=\left(a+b\right)\cos \left(x+c\right)+y-\left(a+b\right)\sin \left(x+c\right)$

$\frac{dy}{dx}-y=\left(a+b\right)\left[\cos \left(x+c\right)-\sin \left(x+c\right)\right]$

Differentiating, we get

$\frac{d^{2}y}{d{x}^2}-\frac{dy}{dx}=-\left(a+b\right)\left[\sin \left(x+c\right)+\cos \left(x+c\right)\right]$

$\frac{d^{3}y}{d{x}^3}-\frac{d^{2}y}{d{x}^2}=-\left(a+b\right)\left[\cos \left(x+c\right)-\sin \left(x+c\right)\right]$

i.e. $\frac{d^{3}y}{d{x}^3}-\frac{d^{2}y}{d{x}^2}=-\frac{dy}{dx}+y$

Hence, order of differential equation is $3$