2.4.3.4 Sympy
from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + y(x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 
ValueError : ODE x*Derivative(y(x), x) + y(x) does not match hint 1st_power_series
 
Python version: 3.12.3 (main, Aug 14 2025, 17:47:21) [GCC 13.3.0] 
Sympy version 1.14.0
 
classify_ode(ode,func=y(x)) 
 
('factorable', 'separable', '1st_exact', '1st_linear', 'Bernoulli', '1st_homogeneous_coeff_best', '1st_homogeneous_coeff_subs_indep_div_dep', '1st_homogeneous_coeff_subs_dep_div_indep', 'almost_linear', 'lie_group', 'nth_linear_euler_eq_homogeneous', 'separable_Integral', '1st_exact_Integral', '1st_linear_Integral', 'Bernoulli_Integral', '1st_homogeneous_coeff_subs_indep_div_dep_Integral', '1st_homogeneous_coeff_subs_dep_div_indep_Integral', 'almost_linear_Integral')