d := 0.0002
kappa := 0.4
k__s := 2.5*d

Um := 3.266825770

Tp := 1.62476126

omega := 2*Pi/Tp

U0 := Um*sin(omega*t)

U := Uf*ln(30*y/k__s)/kappa;
delta := solve(Uf*ln(30*delta/k__s)/kappa = U0, delta);

t0 := 0.001*Tp;

ODE := diff(int(U, y = 0 .. delta), t) = delta*diff(U0, t) - Uf^2;
ICs := Uf(t0) = 0.001*Um;
 

dsn1 := dsolve({ICs, ODE}, Uf(t), numeric);