I'm still a bit new to sage math and I don't understand the result given by desolve_system, here is my code
t = var('t')
var('w C1 C2 C3 n ')
H = function('H')(t)
phi = (C2 * t + C3)^n #function('\\phi')(t)
sigma = function('\\Sigma')(t)
V = C*phi^2#function('V')(phi)
P = function('P')(t)
######
de1 = H^2-w/6 * (P/phi)^2 - V/(6*phi) - 2*sigma/3 + H*P/phi
de2 = diff(H, t) + w/6 * (P/phi)^2 - V/(3*phi) + 2*sigma/3 + 2*H^2 - 1/(2*phi) * (phi * diff(V, t) - 2*V)/(2*w+3)
de3 = diff(phi, t) == P
des = [de1, de2, de3]
######
vars = [H, sigma, P]
sol= desolve_system(des, vars, ivar = t)
And it gives solutions of the form
$$\newcommand{\Bold}[1]{\mathbf{#1}}P\left(t\right) = \mathcal{L}^{-1}\left(\frac{C_{2}^{n} n e^{\left(\frac{C_{3} g_{63262}}{C_{2}}\right)} \Gamma\left(n, \frac{C_{3} g_{63262}}{C_{2}}\right)}{g_{63262}^{n}}, g_{63262}, t\right)$$
I'm not so sure what is the $\mathcal{L}$ in this case, nor the $g_{63262}$ terms. What am I looking at. I have found no information online, maybe because I wasn't sure how to describe this properly.
Thank you.
