Compact output of solution of DE

asked 2015-03-24 15:51:52 -0500

Photon gravatar image

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...

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Comments

This is the standard output form from Maxima (the engine that does such symbolics inside Sage). Various combos using log_simplify('all') and expand_* didn't help, though...

kcrisman gravatar imagekcrisman ( 2015-03-24 20:05:13 -0500 )edit