2-7. (a) please

= = 2-6. Obtain the solution Y(t), as a deviation from its initial steady-state condition y(0), of the following differential equations. Use the method of Laplace transforms and partial fractions expansion. The forcing function is the unit step function, X(t) = u(t). dy(t) (a) + 2y(t) = 5x(t) + 3 dt (b) 9 d2(t) dy(t) + 18 + 4y(t) = 8x(t) - 4 dt dt dy(t) + 4y(t) = 8x(t) - 4 dt2 dt (d) 9 Hyt) dy(t) + 4y(t) = 8x(t)- 4 d-y(1) dy(t) (e) 2 7 +9y(t) = 3x(t) dt3 dt2 dt 2-7. Repeat Problem 2-6(d) using as the forcing function (a) X(t) = (-1/3 (b) X(t) = ult - 1)e-(1-1)/3 (C) 922014 + 9 + 12 dt d12 dy(t) + 21