The order of the differential equation $\frac{d^{2}y}{d{x}^2}-2{\left(\frac{dy}{dx}\right)}^3+\sin \left(\frac{dy}{dx}\right)+y=0$, is $l=2$.

And the degree of the differential equation 

${\left(1+\frac{d^{2}y}{d{x}^2}\right)}^{\frac{2}{3}}={\left[2-{\left(\frac{dv}{dx}\right)}^3\right]}^{\frac{3}{2}}$, is $m=8$.

Now from $y=A{x}^l+B{e}^{mx}$, we get, 

$y=A{x}^2+B{e}^{8x}$

$y^{\text{'}}=2Ax+8B{e}^{8x}$

$y^{\text{'}\text{'}}=2A+64B{e}^{8x}$

i.e. $\left(2x^2-x\right)y^{\text{'}\text{'}}-\left(8x^2-1\right)y^{\text{'}}+(16x-4)y=0$