In the following differential equation, the numerically obtained value of , at , is __________ (Round off to 2 decimal places).

A differential equation  has to be solved using trapezoidal rule of integration with a step size h = 0.01s. Function u(t) indicates a unit step function.  If , then value of x at t = 0.01s will be given by:

The differential equation is discretized using Euler's numerical integration method with a time step ΔT > 0.  What is the maximum permissible value of ΔT to ensure stability of the solution of the corresponding discrete time equation?

A system governed by the differential equation  is initially at rest. Determine the value of y at t=0.1s using the trapezoidal rule of integration with a step size of 0.05s