Error convergence plot: Finding the exact and numerical solution of an ODE using different timesteps and plotting the error between these solutions Vs the different discretization or timesteps.

I'm trying to iterate through different timesteps and solving both the exact and numerical solution to a an initial value ordinary differential equation. I'm using the L2 error norm method to find the error between my analytical and numerical solution and then plotting the error vs the different timesteps. However, for some reason my code does not give me the accurate exact solution results. Also, my error seems to increase with discretization/timestep which is wrong. Can you please help me? Here is my code:

function [error_y1,Exact,Numerical] = Conv

clear all;

clear; clc;

tic;

%% Exact (analytical) solution function

syms y(x);

Dy =diff(y);

ODE =diff(y,x,2) == -4*diff(y,x)-(8*(y));

ODE=diff(y,x,2) == -4*diff(y,x,1)- (8*(y));

cond1 =y(0)==1; cond2=Dy(0)==0;

conds=[cond1 cond2];

ySol(x)=dsolve(ODE,conds);

ySol=simplify(ySol);

Exact=ySol;

%% Setting up and iterating through both exact and numerical solution

%Setting up time-step and number of iteration per timestep

y0 = 1; % initial condition

m_list = 10:10:100; % number of iterations to get to t=1

h_list = 1./m_list; % step size

n = length(m_list);

error_y1 = zeros(1,n); % to hold the final point

Exact=zeros(1,n);

Numerical=zeros(1,n);

sum=0;

for i=1:n % loop over different step sizes

m = m_list(i); % get the number of iterations

h = h_list(i); % get step size

y1 = y0; % start with y(0)

for t=1:m % iterating through euler and exact solution

y1_list=@(h) (1+h)*y1; % Euler solution iteration begins here

Exactf=@(h) double(ySol(h)); % Exact solution iteration begins here

Exact(i)=double(Exactf(h));

Numerical(i)=double(y1_list(h));

f =@(h) ((y1_list(h)-Exactf(h))^2);

% set up to iterate throughnumerical integration of the function f

for u=1:1:m-1

e(u)=0+(u*h);

k(u)=f(e(u));

sum=sum+f(u);

end

% numerical integration using trapezoidal method begins from here.

err=h/2*(f(0)+f(1)+2*sum);

err2=sqrt(err/m);

error_y1(i)=double(err2);

end

end

%% Plotting exact solution & numerical solution Vs discretization on the same graph

plot (h_list,Exact, '-or');

hold on

plot (h_list,Numerical, '-xb');

%% Plotting log error Vs log discretization

subplot(121);plot(h_list, error_y1, '-o')

title('error -- h');xlabel('h');ylabel('error')

subplot(122);loglog(h_list, error_y1, '-o')

title('log(error) -- log(h)');xlabel('log(h)');ylabel('log(error)')

toc;

end