When I'm trying to solve DE:
t = var('t')
y = function('y', t)
de = t*(y^2)*diff(y,t) + y^3 == 1
sol = desolve(de,[y,t], [1,2])
the output is pretty ugly:
-1/3*log(y(t)^2 + y(t) + 1) - 1/3*log(y(t) - 1) == -1/3*log(7) + log(t)
When I'm solving this in matlab:
clear;
syms y(t)
y(t) = dsolve(t*(y^2)*diff(y,t) + y^3 == 1, y(1) ==2)
The output looks much better:
y(t) = (exp(log(7) - 3*log(t)) + 1)^(1/3)
Can I see output in sage looking similiar to this from matlab? Simplify(sol) dosen't work. Maybe I've made mistake somewhere, but I can't determine without knowing the form y(t) from sage.
And btw, typing:
t*(y^2)*y'+ y^3 = 1, y(1) = 2
into wolframalpha.com results yet another solution. I'm lost...
