$6\mathrm{.}53$ Develop a differential equation for $i_L(t)$ in the circuit of Fig. P$6\mathrm{.}53.$ Solve it to determine $i_L(t)$ for $t0$ subject to the following element values: $I_s=36A,R_s=100k,R=100,L=10mH,$ and $C=10F.$

Figure P$6\mathrm{.}53$: Circuit for Problem $6\mathrm{.}53.$