(Solved): In the circuit shown below, the switch in the circuit is moved, as shown, from open to close at t=0 ...

In the circuit shown below, the switch in the circuit is moved, as shown, from open to close at $t=0$. The voltage $V_1(t)$ labeled in the circuit has the form $V_1(t)=k_1{e}^{?at}+k_{2}V,t?0$; the current $I_1(t)$ across the resistor $R_2$ has the form $I_1(t)=k_3{e}^{?at}+k_{4}mA,t?0$. Compute $k_1,k_2,k_3,k_4,a$. Assume $V_{\text{in }}=20\mathrm{V},R_1=100\mathrm{k}?,R_2=100\mathrm{k}?,R_3=50\mathrm{k}?,C_1=1?F$. Also assume zero initial conditions for the capacitor.