Can't use math lab show workings
Can't use math lab show workings Differential Equation The following ordinary differential equation is to be...
The differential equation : dy/dx = 2x -3y , has the initial conditions that y = 2 , at x = 0 Obtain a numerical solution for the differential equation, correct to 6 decimal place , using , The Euler-Cauchy method The Runge-Kutta method in the range x = 0 (0.2) 1.0
answer please , Cauchy problem Exercise 4. Find all solutions of the following differential equation, after determining its domain sin y (-1) Moreover, find the solution to the Cauchy problem with initial data y(0) sketch its graph. Finally, study the behaviour of the function thus obtained at r determining its order of infinitesimal or infinite, if defined. 2 and 1 Exercise 4. Find all solutions of the following differential equation, after determining its domain sin y (-1) Moreover, find the...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
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...
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Question 20 1 pts Problem 20: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: H+ 15y =t 1.C:y(0) = 0.5 Carry out two consecutive steps of the Euler solution from the initial condition with a time step of At = 0.2. and the predicted solutions are None of the above. y(0.2)--0.25 and y(0.4)-0.13 (0.2)-0.05 and y(0.4)-0.03 y(0.2) -- 1.00 and y(0.4)-2.04 y(0.2)-0.13 and y(0.4)-0.20
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial value problem GE:+15y = 1.C:y(0) -0.5 Carry out two-steps of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.1. and the predicted solutions is y(0.2)-0.20 None of the above. y(0.2) - -0.75 y(0.2)-1.27 y(0.2)=0.25
Hello! I need help with this college level differential equations question. Please show work and thank you. 3. Consider the initial value problem y' (t) 1 0y(t) y(0) Clearly, the solution to the system is y(t) = et and 2(t) = e-10 t. Suppose we tried solving the system using forward Euler. This would give us with to 0, y(to) 1, and z(to-1. a. Show that the numerical solution for z(t) will only tend to zero if Δι < 2...
MATLAB HELP 3. Consider the equation y′ = y2 − 3x, where y(0) = 1. USE THE EULER AND RUNGE-KUTTA APPROXIMATION SCRIPTS PROVIDED IN THE PICTURES a. Use a Euler approximation with a step size of 0.25 to approximate y(2). b. Use a Runge-Kutta approximation with a step size of 0.25 to approximate y(2). c. Graph both approximation functions in the same window as a slope field for the differential equation. d. Find a formula for the actual solution (not...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...