3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t),...
Help me plss!! 3. Consider the initial value problem dy Solve the initial value problem for є-0, to obtain y(t)-3e-21 Using the method of perturbations, setting y yoey, find the first-order correction, y,(t), for the initial value problem with € 0 and є is a small parameter.
Problem 3. Given the initial conditions, y(0) from t- 0 to 4: and y (0 0, solve the following initial-value problem d2 dt Obtain your solution with (a) Euler's method and (b) the fourth-order RK method. In both cases, use a step size of 0.1. Plot both solutions on the same graph along with the exact solution y- cos(3t). Note: show the hand calculations for t-0.1 and 0.2, for remaining work use the MATLAB files provided in the lectures Problem...
Need help with this MATLAB problem: Using the fourth order Runge-Kutta method (KK4 to solve a first order initial value problem NOTE: This assignment is to be completed using MATLAB, and your final results including the corresponding M- iles shonma ac Given the first order initial value problem with h-time step size (i.e. ti = to + ih), then the following formula computes an approximate solution to (): i vit), where y(ti) - true value (ezact solution), (t)-f(t, v), vto)...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations together with initial conditions with step size 0.1: 2. dt t+x 3. dx dt = y, dy dt x(0) = 1.2 and --ty +xt2 + y(o) 0.8 Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h...
Using Laplace transforms, solve the initial value problem y' = 2y + 3e-t, y(0) = 4, where y' = Note: to check your work, this equation is linear so it is possible to solve using integrating factors also. 17 Marks) Y
Q2 Using Fourth-order RK method, solve the following initial value problem over the interval from t = 0 to 1. Take the initial condition of y(0) = 1 and a step size (h)=0.5. dy = f(t, y) = y t- 1.1 y dt
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
Using the Runge-Kutta fourth-order method, obtain a solution to dx/dt=f(t,x,y)=xy^3+t^2; dy/dt=g(t,x,y)=ty+x^3 for t= 0 to t= 1 second. The initial conditions are given as x(0)=0, y(0) =1. Use a time increment of 0.2 seconds. Do hand calculations for t = 0.2 sec only.
(3.) Consider the following nonlinear, first-order initial value problem +y+sin(E)y2 =0, y(0)=1 Obtain the two-term asymptotic expansion of the solution for 8 0 .
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...