Transient analysis of op-amp circuit
Let the op amp output voltage be \$v_o\$

At the inverting input, \$v^-=0\$ since it's a virtual earth.

Therefore, KCL at the \$ v^-\$ node gives:

$$ C\frac{dv_o}{dt}+\frac{v_o}{R_2}=0$$
or
$$ \frac{dv_o}{dt}+\frac{v_o}{R_2C}=0$$

Solving this ODE:

$$ v_o=Ae^{-t/R_2C}$$

Initial condition: $$ t=0,\: v_o=4$$

Hence \$A=4\$, and:

$$ v_o=4e^{-t/R_2C}=4e^{-2t}$$