QUESTION 9 Consider given ordinary differential equation, y"+y" - 2y = 0, y(t = 0) =...
3. Given the ordinary differential equation: (x-2y) dx And the initial condition y(0) = 1, approximatey(0.5) using the Heun method and step sizes of 0.25.
Assignment 2 Q.1 Find the numerical solution of system of differential equation y" =t+2y + y', y(0)=0, at x = 0.2 and step length h=0.2 by Modified Euler method y'0)=1 Q.2. Write the formula of the PDE Uxx + 3y = x + 4 by finite difference Method . Q.3. Solve the initial value problem by Runga - Kutta method (order 4): y" + y' – 6y = sinx ; y(0) = 1 ; y'(0) = 0 at x =...
4. Find the solution to the differential equation y"+2y'+ 2y-S(t-) y(0) 0, y (0)-0 and graph it.
Consider the following ordinary differential equation: y' - sin(4t) = 0 (Eq. 4) The boundary condition is that y(0) = -0.25. When the position y is a function of time, t, this describes an oscillating system – it's an example of simple harmonic motion. Functions like this are extremely common when considering mechanical systems. Write MATLAB code to carry out the following tasks: a) Apply the Taylor method for solving this equation (up to t4) for 20 steps, using a...
Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the boundary value problem for the general second-order equation with constant coefficients d2y dy dr2 dr Let the interval a x approximations b be divided inton subintervals of width h -(b- a)/n. Using the central difference find the linear system that must be solved to approximate y2.y3.....yn Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the boundary value...
Write a MATLAB code to solve below 2nd order linear ordinary differential equation by finite difference method: y"-y'-0 in domain (-1, 1) with boundary condition y(x-1)--1 and y(x-1)-1. with boundary condition y an Use 2nd order approximation, i.e. O(dx2), and dx-0.05 to obtain numerical solution. Then plot the numerical solution as scattered markers together wi exp(2)-explx+1) as a continuous curve. Please add legend in your plot th the analytical solution y-1+ Write a MATLAB code to solve below 2nd order...
The function Y(t) = t is a solution of the differential equation (t2+4)y" - 2ty' + 2y = 0. Find a real general solution of this equation.
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Find the particular solution such that y=0 when t=0 of the differential equation: (dy/dt) - 2y = t
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2