5. [-/0.37 Points] DETAILS ZILLDIFFEQMODAP11 7.6.009. 0/15 Submissions Used Use the Laplace transform to solve the given system of differential equations. d2x + day = + 2 dt2 dt2 d2 x dt2 dt2 = 3t x(0) = 7, x'(0) = 0, y(0) = 0, y'(0) = 0 X(t) = y(t) = Need Help? Read ItL1 d12 + Riz + Ri3 = E(t) dt L2 di3 + Riz + Riz = E(t). dt Ki, R 712 i3 E L2 By Kirchhoff's first law we have the following relationship between /1, i2, and i3. /1 = in + 13 By applying Kirchhoff's second law to the /1, i2 loop, we obtain the following. E(t) = R /1 + 1 L1 12 By applying Kirchhoff's second law to the /1, /3 loop, we obtain the following. E(t) = R 11+ 12 13' Writing /1 in terms of /2 and i3 and rearranging terms, one obtains the given system. (b) Solve the system in part (a) if R = 5 0, L1 = 0.025 h, L2 = 0.02 h, E = 200 V, 2(0) = 0, and /3(0) = 0. 8000 + 12(t) = 13(t) = X (c) Determine the current /1 (t). i1(t) =9. [0.18/0.37 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 7.6.017. 7/15 Submissions Used MY NOTES Solve the system given in (17) of Section 3.3 L1- dt diz + (R1 + R2)i2 + R113 = E(t) (17) di3 L2 dt + R1i2 + R1/3 = E(t) when R1 = 6 0, R2 = 5 0, L1 = 1 h, L2 = 1 h, E(t) = 52 sin t V, i2(0) = 0, and /3(0) = 0. 904 -2t + 30 -15t 754 442 12(t) = 565 e 113 565 cos ( t) + 565 sin (t) 8136 -2t 120 -15t 25272 565 sin (t) - 8736 13(t) = + 113 565 cost) X 565 Need Help? Read It10. [0/0.42 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 7.6.019. 9/15 Submissions Used MY NOTES Solve the following system of equations (given in (5) of Section 7.6) when E = 80 V, L = 2 h, R = 50 0, C = 10-4f, /1(0) = 0, and /2(0) = 0. L a1 + Riz = E(t) dt RC 12 + 12 - 11 = 0 dt i1(t) = i2(t) = Need Help? Read It