Let $\mathrm{H1},\mathrm{H2}$ be hyperexponential functions of x over a field K of characteristic 0. The AreSimilar(H1,H2,x) command returns true if $\mathrm{H1}\left(x\right)$ and $\mathrm{H2}\left(x\right)$ are similar. Otherwise, it returns false.

H1 and H2 are similar if their ratio can be written as the product of a rational function and a constant in some extension of K.

with(DEtools):

H :=  exp(Int((2*x-7)/(x+4)^2,x))*(x^6+16*x^5+103*x^4+
327*x^3+647*x^2+737*x+194)/(x-1)^2/(x+2)^4/(x+4)^2;

$H≔\frac{{\ⅇ}^{\int \frac{2x-7}{{\left(x+4\right)}^2}\ⅆx}\left(x^6+16x^5+103x^4+327x^3+647x^2+737x+194\right)}{{\left(x-1\right)}^2{\left(x+2\right)}^4{\left(x+4\right)}^2}$

(H1,H2) := ReduceHyperexp(H,x):

H1;

$-\frac{\left(24x^3+143x^2+292x+216\right){\ⅇ}^{\int -\frac{15}{{\left(x+4\right)}^2}\ⅆx}}{\left(x-1\right){\left(x+2\right)}^3}$

H2;

$\frac{\left(x^3+17x^2+88x-231\right){\ⅇ}^{\int \frac{-23-2x}{{\left(x+4\right)}^2}\ⅆx}}{x-1}$

AreSimilar(H,H2,x);

$\mathrm{true}$

AreSimilar(H1,H2,x);

$\mathrm{true}$

Geddes, Keith; Le, Ha; and Li, Ziming. "Differential rational normal forms and a reduction algorithm for hyperexponential functions." Proceedings of ISSAC 2004. ACM Press. (2004): 183-190.