Answer Happy

EE2006/IM2006 (b) (1) Consider the initial-value problem ty-√ty+2y=Int, (10) L (10)-0.5 where y" a- and y'a Use Heun's method with step size h-0.1 to compute approximate values of y(10.2) and y'(10.2). Write down the formulae of your method explicitly. (ii) Comment on the advantages and disadvantages of the following methods for solving differential equations: Euler, Heun's and Runge-Kuttar. (13 Marks) 3. (a) Using the basic properties of Laplace transform and the Laplace transform table, (1) Find the Laplace transform of f(t)=6r²u(t-1) (ii) Find the inverse Laplace transform of +9s+2 F(1) = (-1) (+3) (14 Marks) (b) An industrial process is described by the following second-order differential equation dy(1) +2- +5y(t)=xt), 120 dt where y(r) is the output variable and a() is the input variable. Assume that the initial conditions are y(t) = 0 and $(1) dr -=0, at = 0 Using the method of Laplace transform, determine the output y(t) if x(t) is the difference of two delayed unit-step functions as follows x(t)=(1-10)-(-20) (11 Marks) 3