3-17. Solve the following differential equations by means of the Laplace transform. (a) d2f(t) df (t) +5 +4f(t) = eu¸(t) (Assume zero initial conditions.) dt² dt dx,(t) -=x₂(t) dt (b) dx2(t). dt = −2x₁(t)−3x2(t)+us(t)x₁(0)=1,x2(0)=0 [d³y(t)¸¸ d² y(t)¸ dy(t) +2 dt² dt² (c) d²y (0)=-1 dt dt² + +2y(t)=−e¯¹u¸(t) dt dy (0)=1y(0)=0 3-24. Express the following set of first-order differential equations in the vector-matrix form of Ax(t)+ Bu(t). -=-x₁(t)+2x2(t) dx(t) = dt dx,(t) dt dx2(t) (a) dt dx,(t) dt dx,(t) = =−2x2(t)+3x3(t)+u(t) = −x(t)−3x2(t)− x¸(t)+u₂(t) == −x₁(t)+2x₂(t)+2u₁(t) dt dx,(t) (b) -=2x(t)−x,(t)+u,(t) dt dx,(t) = 3x₁(t) −4x2(t) − x(t) dt