Infinite initial conditions in ODE and arbitrary constant

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Is it possible to include infinite initial conditions in an ODE? For example,

ode_soln = desolve(ode, q, ics[0, -Infity])

throws and error.

Alternatively, I can leave the initial condition blank:

ode_soln = desolve(ode, q)
soln = solve(ode_soln, q)
show(soln[0])

Then output Includes an arbitrary constant written C $$ q\left(t\right) = -\frac{p}{C {\left(p + 1\right)} + {\left(p + 1\right)} t} $$

I tried to set a value for $C$ via,

show(soln[0].substitute(C = 0))

but it made no difference. Here $p$ I declared as a variable, and I can do things like

show(soln[0].substitute(p = 1))

to produce the expected output

$$ q\left(t\right) = -\frac{1}{2 {\left(C + t\right)}} $$

So it seems that I need to refer to the arbitrary constant by some other name than $C$. How can I do this?