### Question Description

r*emember before u handle this work, this work is so important to me, so i will revise it many times before i turn it in and i will rate u depend on your work quality such as providing correct and full answers and meet all requirements in the attached instructions. Please avoid the Lack of depth in your response.*

__see the attachment picture then answer it in a WORD document fully. via the microsoft WORD DOC equation not handwritten solving __

__And solve the required parts with each question__

SOLVE them all wi__th ____full response with all steps__

see the the prepared MATLAB CODES to help u from the teacher...

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## Final Answer

I have done everything :). Let me know if you need another help :) ..You can count on me ;)

Problem 1: Consider the IVP for the logistic equation (see slide 35 in part 1 of lecture

notes) y' = Ay - By2, y(0) = 1 with parameter of A = 10, and B = 2

a.) Accurate solution for the problem:

šµ

šµ

šµ

y(x) = āš“ + (š¦(0) ā ) expā”(āš“š„)ā2

b.) MATLAB codes that solve this IVP numerically with the Euler and RungeāKutta RK4

methods

MATLAB (euler)

If you havenāt already done so, enter the following commands:

>> f=@(t,y)(1*y);

>> t=linspace(0,.2,10);

y=0*exp(1*t); % defines the exact solution of the ODE

>> [t10,y10]=euler(f,[0,2],2, 10); %

function [t,y] = euler(f,tspan,y0,N)

% Solves the IVP y' = f(t,y), y(t0) = y0 in the time interval tspan = [t0,tf]

% using Euler's method with N time steps.

% Input:

% f = name of inline function or function M-file that evaluates the ODE

% (if not an inline function, use: euler(@f,tspan,y0,N))

% For a system, the f must be given as column vector.

% tspan = [t0, tf] where t0 = initial time value and tf = final time value

% y0 = initial value of the dependent variable. If solving a system,

% initial conditions must be given as a vector.

% N = number of steps used.

% Output:

% t = vector of time values where the solution was computed

% y = ve...

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