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t = var('t')
x = function('x')(t)
expr = diff(x,1) == 1 + x / (1+t)
show(expr)
∂∂tx(t)=x(t)t+1+1\displaystyle \frac{\partial}{\partial t}x\left(t\right) = \frac{x\left(t\right)}{t + 1} + 1
sol = desolve(expr, x, ics=[0, 0])
show(sol)
(t+1)log⁡(t+1)\displaystyle {\left(t + 1\right)} \log\left(t + 1\right)
werte = solve(sol == 100 * (1+t), t)
werte
[t == e^100 - 1, t == -1]

Wie lange ist das?

t_sol = werte[0].rhs().n()
time = t_sol * units.time.second
time.convert(units.time.year)
8.52396353949815e35*year 
(100 * (1 + t_sol) * units.length.centimeter).convert(units.length.light_year)
2.84134206085552e27*light_year