Mechanical engineering

Determine the total response of the 2nd-order linear differential equation using analytical method with initial conditions, 𝑦(0)=1 𝑎𝑛𝑑𝑦(0)=2𝑦+6𝑦+5𝑦=10sin2𝑡Determine the characteristic equation and root, the homogeneous solution yH(t), the particular solution yP(t) and the total solution y(t). Plot the homogeneous, particular and total solution with MATLAB.2. Determine the total response of the 2nd-order linear differential equation using analytical method with initial conditions, 𝑦(0)=1 𝑎𝑛𝑑𝑦(0)=2𝑦+6𝑦+5𝑦=10Determine the characteristic equation and root, the homogeneous solution yH(t), the particular solution yP(t) and the total solution y(t). Plot the homogeneous, particular and total solution with MATLAB.3. Determine the total response of the 2nd-order linear differential equation using Laplace method with initial conditions, 𝑦(0)=1 𝑎𝑛𝑑𝑦(0)=2U(t)𝑦+6𝑦+5𝑦=10U (t) is a unit step function, which has a value of one when it is greater than 0.(1) Using Laplace transform to determine the system response in the s domain Y(s). (2) Determine the poles of the system response Y(s). (3) Using inverse Laplace transform to determine the system response y(t).(4) Find the steady state result from Y(s) and y(t).