Problem Solution of Differential Equations using the Laplace Transform. Case #2: Repeated Roots. (Handout, pages 13-16 of 48) Use the method of Laplace transforms and partial fractions expansion to obtain the solution Y(t), as a deviation from its initial steady-state condition y(0), of the following differential equations. The forcing function is the unit step function, x(t) = u(t). dy) 18 dt2 dy(t) + 24 dt - 5 + 8 y() = 8x(1) d'y(t) 9 dy(D) + 6 dt + x(t) = 2x(t) + 3 dt2