Given the differential equation i + x = 0 with initial condition x()-x(t-0)-4,0 s 5. ntial...
please answer b. and c. Problem 1. Consider the differential equation given by (a) On the axes provided below, sketch a slope field for the given differential equation at the nine points indicated. locales de mor t e wold qolution to the given differential equation with the initial condition (b) Let y = f(x) be the particular solution to the given differential equation with the initial condition f(0) = 3. Use Euler's method starting at x = 0, with a...
Please show Matlab code and Simulink screenshots 2. Differential Equation (5 points) Using (i) Euler's method and (ii) modified Euler's method, both with step size h-0.01, to construct an approximate solution from t-0 to t-2 for xt 2 , 42 with initial condition x(0)-1. Compare both results by plotting them in the same figure. 3. Simulink (5 points) Solve the above differential equation using simplink. Present the model and result. 2. Differential Equation (5 points) Using (i) Euler's method and...
(15 points) This problem is related to Problem 7.23-24 in the text. Given the differential equation"+20 5v (cos(9 t)u(t) Write the matrix equation for using Euler's method to compute v(t +h) from information of the function at time t, i.e., you know v(t) and initial conditions. It is assumed you will use two auxiliary functions, vi() and u2) vi(t+ h) v2(t+h vi(t) tr(t) vi (t) u2(t) For h-0.1, compute the solution for ț-0, 0.1, 0.2, 0.3, when the initial conditions...
Consider the following initial value problem у(0) — 0. у%3D х+ у, (i) Solve the differential equation above in tabular form with h= 0.2 to approximate the solution at x=1 by using Euler's method. Give your answer accurate to 4 decimal places. Given the exact solution of the differential equation above is y= e-x-1. Calculate (ii) all the error and percentage of relative error between the exact and the approximate y values for each of values in (i) 0.2 0.4...
Using MATLAB_R2017a, solve #3 using the differential equation in question #2 using Simulink, present the model and result. 2. Differential Equation (5 points) Using (i) Euler's method and (ii) modified Euler's method, both with step size h-0.01, to construct an approximate solution from F0 to F2 for xt 2, 42 with initial condition x(0)=1. Compare both results by plotting them in the same figure. 3. Simulink (5 points) Solve the above differential equation using simplink. Present the model and result....
Consider the partial differential equation together with the boundary conditions u(0, t) 0 and u(1,t)0 for t20 and the initial condition u(z,0) = z(1-2) for 0 < x < 1. (a) If n is a positive integer, show that the function , sin(x), satisfies the given partial differential equation and boundary conditions. (b) The general solution of the partial differential equation that satisfies the boundary conditions is Write down (but do not evaluate) an integral that can be used to...
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic
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.
The function u(x, t) satisfies the partial differential equation with the boundary conditions u(0,t) = 0 , u(1,t) = 0 and the initial condition u(x,0) = f(x) = 2x if 0<x<} 2(1 – x) if}<x< 1 . The initial velocity is zero. Answer the following questions. (1) Obtain two ODES (Ordinary Differential Equations) by the method of separation of variables and separating variable -k? (2) Find u(x, t) as an infinite series satisfying the boundary condition and the initial condition.
1 with 5. Consider the differential equation y, f(x,y) with initial condition y(zo) = yo. Show that, zi = zo +h, the solution at x1 can be obtained with an er ror O(h3) by the formula In other words, this formula describes a Runge-Kutta method of order 2. with 5. Consider the differential equation y, f(x,y) with initial condition y(zo) = yo. Show that, zi = zo +h, the solution at x1 can be obtained with an er ror O(h3)...