# Take limit in NDSolve

I have this equation :

eqkk =
D[k[t], {t,2}] - ((3 sola'[t]/sola[t]) + (3 sola''[t]/sola'[t]) -
(1/(sola'[t] sola[t]^2))) D[k[t], t]


To get $$k(t)$$:

solk = NDSolveValue[{eqkk == 0, k[0] == 1, k'[0] ==0}, k, {t, tmin,tmax}]


Now I want to evaluate solk, not at k'[0] == 0, but to take the limit of solk as k'[0] -> 0

### Edit

sola[t] is another function solved before with NDSolveValue as well. Consider for instance sola[t] is like y[t]

Any help appreciated.

• What's sola[t]? May 18 '19 at 9:11
• I edit the question. May 18 '19 at 9:20
• It might be easier for people to help you if you provide the code that defines sola[t]. May 18 '19 at 9:30
• Wouldn't it be easier to solve the system of ode's in {k[t],sola[t]} in one step? May 18 '19 at 10:10
• @Dr.phy Use solk = ParametricNDSolveValue[{eqkk == 0, k[0] == 1, k'[0] == p}, k, {t, tmin, tmax}, {p}], then the function solk[p][t] has a limit solk[0][t]`. May 18 '19 at 11:26