Question about differential equation

Hi,

i have the following equation

dk(s,t)/dt = ct^a * [ k(s,t)+A ] / [ \integral_0^{t} (k(u,t)+A) du ]

where c, a and A are constants. The resulting function k(s,t) is

k(s,t) = A * (t/s)^{a+1}

under the conditions k(s=0,t=0)=0 und k(s=t,t)=0

My question is, is this an ordinary or a partial differential equation?
i am confused by the s and t in the equation (which makes it partial to
me), but on the other hand, k is only differentiated to t, not to s.

Can someone help?

.