Where am I going wring with the following Python code on sage math?

Question

I am trying to solve the following system of equations but am not sure where I am going wrong with my code. I am new to writing in this language and am not sure why in my output I am getting "ilt" (not sure what this means) as well as where the g's in the output came from. I have used this exact code with a different system of functions and have gotten answers that are normal. Is there something wrong with how I put the code in or am I just not reading the output properly?

My code is: (Used on Sage math)

t = var('t') 
y = function('y')(t) 
x = function('x')(t) 
z = function('z')(t)

de1 = diff(x, t) == ((38/100)-(20/1800))*x + (1088/87500)*y + 0*z + 49.3
de2 = diff(y, t) == (20/1800)*x + ((-1088/87500)-(1/100)-(353/21875))*y + (7/200000)*z
de3 = diff(z, t) == 0*x + (1/100)*y - (7/200000)*z

desolve_system([de1, de2, de3], vars = [x, y, z], ics = [0, 0, 0, 0])

This gives the following output:

[x(t) == ilt(13865625/21022*(39375000000*g3242^2 + 1710528125*g3242 + 1950039)/(196875000000*g3242^3 - 65024359375*g3242^2 - 2830795000*g3242 - 73577), g3242, t) - 2773125/21022,
 y(t) == ilt(1348046875/42044*(315000000*g3242^2 - 104038975*g3242 - 1165752)/(196875000000*g3242^3 - 65024359375*g3242^2 - 2830795000*g3242 - 73577), g3242, t) - 2156875/42044,
 z(t) == ilt(96289062500/10511*(315000000*g3242^2 - 104038975*g3242 - 4529272)/(196875000000*g3242^3 - 65024359375*g3242^2 - 2830795000*g3242 - 73577), g3242, t) - 154062500/10511]

Answer 1

I'm just interpreting what I see.

Your solution requires the eigenvalues of the system matrix, the roots of a cubic polynomial. g3242 is the generator of a 6-dimensional algebra over the rationals that contains all the roots. One could reduce the rational functions, which probably are the exponent factors of the solution basis exponentials, to polynomials of degree 5, but the cost would be much larger coefficients.

ilt and g3242 are internals of the underlying CAS system that should be resolved on the front-end. Do you use the most recent version of all the software in this bundle?