Question: How do I use dsolve to numerically solve a differential equation that contains an Interpolation function

The following is a simple example of what I would like to do: 

M := Array(1 .. 10, 1 .. 2);

for i to 10 do
    M[i, 1] := i;
    M[i, 2] := 3*i;
end do;

Mt := Interpolation:-LinearInterpolation(M);
E := t -> Mt(t);
diffeq := D(C)(t) = E(t);
dsolve({diffeq, C(0) = 0}, {C(t)}, numeric);
Error, (in dsolve/numeric/process_input) unknown Interpolation:-LinearInterpolation([Vector(10, [1.,2.,3.,4.,5.,6.,7.,8.,9.,10.], datatype = float[8], attributes = [source_rtable = (Vector(10, [1.,2.,3.,4.,5.,6.,7.,8.,9.,10.], datatype = float[8], attributes = [source_rtable = (Array(1..10, 1..2, [[1.,3.],[2.,6.],[3.,9.],[4.,12.],[5.,15.],[6.,18.],[7.,21.],[8.,24.],[9.,27.],[10.,30.]], datatype = float[8]))]))])],Vector(10, [3.,6.,9.,12.,15.,18.,21.,24.,27.,30.], datatype = float[8], attributes = [source_rtable = (Array(1..10, 1..2, [[1.,3.],[2.,6.],[3.,9.],[4.,12.],[5.,15.],[6.,18.],[7.,21.],[8.,24.],[9.,27.],[10.,30.]], datatype = float[8]))]),uniform = true,verify = false) present in ODE system is not a specified dependent variable or evaluatable procedure