Op-amp analysis with capacitor
One of the "tricks" I've taught in EE fundamentals class is that placing a network in series with a current source changes the voltage across the current source only.

(This is most easily seen by enclosing the network inside a supernode and applying KCL - the current entering the supernode is the current from the current source and this must equal the current leaving the supernode.)

Thus, the solution for \$v_o(t)\$ is unchanged by replacing the RC network with a wire and then it is clear that this circuit is a current-to-voltage converter with trans-resistance:

$$R_M = -10k \Omega $$

and so, 

$$v_o(t) = -i_s(t) \cdot 10k\Omega$$

The answer given by the book is clearly not for the circuit as drawn.