11 found Use Laplace transforms to find the value of x given that dx 4- + 6x + y = 2 sin 2t dt dx dt and that x = 2 and dx/dt = -2 when t = 0. 30 dr +x= di dt (a) Use Laplace transforms to solve the differential equation dy dt i + = given that 0 = 0 and de/dt = 0 when t = 0. (b) Using Laplace transforms, solve the simultaneous differential equations 3e-2r de +8+160 = sin 2t dt + 2i + 6i = 0 diz dr given that i, = 1, i=0 when t = 0. - -3i = 0