Решение диф. уравнения тремя способами

% nachalnoe uslovie berem: y(0)=1
[T,Y]=ode45('fun',[0,10],1);
% reshenie s solverom:
plot(T,Y,'*r');
% analiticheskoe reshenie:
t=0:.1:10;
a=3;
b=2;
y=a/b*2/3*t.^(3/2)+1;
hold on
plot(t,y);
xlabel('t')
ylabel('y')
legend('ode45','exact solution','Location','NorthWest')

% file funkciia pravaia chast uravneniia:
function f=fun(t,y)
a=3;
b=2;
f=[a/b*t^(1/2)];

dt=0.1;
t=0:dt:10;
a=3;
b=2;
X=a/b*t.^(1/2);
Y(1)=1; % initial condition
for i=1:length(t)-1,
Y(i+1)=Y(i)+X(i)*dt;
end;
plot(t,Y,'om')
 
% analytical solution
y=a/b*2/3*t.^(3/2)+1;
hold on
plot(t,y);
xlabel('t')
ylabel('y')
legend('Euler method','exact solution','Location','NorthWest')

% using feval 
% a=3, b=2, y(1)=1
clear all;
y=feval('dsolve','Dy=3/2*t^(1/2)','y(1)=1','t');
pretty(y)

y=feval('dsolve','Dy=3/2*t^(1/2)','y(0)=1','t');

dt=0.1;
t=0:dt:10;
a=3;
b=2;
X = @(t)a/b*t.^(1/2);
Y(1)=1; % initial condition t(1)=0
for i=1:length(t)-1,
% R.-K. formulas are simplified, 
% because the right side of the equation is independent of y.
k1=dt*X(t(i));
k2=dt*X(t(i)+dt/2);
k3=k2;
k4=dt*X(t(i)+dt);
Y(i+1)=Y(i)+(k1+2*k2+2*k3+k4)/6;
end;
plot(t,Y,'xr')
 
% analytical solution
y=a/b*2/3*t.^(3/2)+1;
hold on
plot(t,y);
xlabel('t')
ylabel('y')
legend('fourth-order Runge–Kutta method','exact solution','Location','NorthWest')

function f=fun(x)
f=x;

t0=0;
tk=1;
h=0.01;
a=5;
b=2;
y=0;
fprintf('--------------------\n');
fprintf('|  t  |  x  |  y  | \n');
fprintf('--------------------\n');
for t=t0:h:tk
x=(a/b)*sqrt(t);
f=fun(x);
y=y+h*f;
fprintf('|%2.2f|%2.2f|%2.2f|\n',t,x,y);
plot(t,x,'g*')
grid on
hold on
plot (t,y,'k*')
end