Please help, I asked my professor what is wrong with my calculation but he cant find my error.

5/8 POINTS PREVIOUS ANSWERS ZILLDIFFEQ8 7.6.015. (a) Show that the system of differential equations for the currents iz(t) and is(t) in the electrical network shown in the figure below is L1 dt diz + Riz + Rig = E(t) L2 dt d13 + Riz + Rig = E(t). R 12 F L2 By Kirchhoff's first law we have the following relationship between 1, i2, and is. 11 = 12+ 13 By applying Kirchhoff's second law to the /1, iz loop, we obtain the following. E(t) = R L1 12 By applying Kirchhoff's second law to the /1, is loop, we obtain the following. E(t) = R 13' Writing i in terms of iz and is and rearranging terms, one obtains the given system. (b) Solve the system in part (a) if R = 10 0, 41 = 0.02 h, 42 = 0.05 h, E = 100 V, /2(0) = 0, and i3(0) = 0. 12 ( t ) = 5 5-70t X 13 (t ) = 2e-7000t X (c) Determine the current i] (t). i1 (t) = 70e - 70t