Any ideas why Euler method isn't running?

I have the following equation: (x^3)y' + 20*(x^2)y = x with y(2)=0

I have to get the Euler code to run and execute. So far this is my code, but the graph looks wrong, and the approximations aren't even showing up.

Script file:

function[T,Y] = euler(f,a,b,ya,h)
a = 0; b = 1;
T = a:h:b;
Y = zeros(1,length(T));
Y(2) = ya;

for k = 1 : length(T)-1
      Y(k+1) = Y(k) + h*f(T(k),Y(k));
end

Code:

%%Part 1 - Euler

% y'(t) = 3*y(t)
% A function file euler.m is needed; you'll do this in the homework

clear all

% define the problem: function f and domain
f = @(t,y) (1/(t^2)) - ((20*y)/t);
a = 2; b = 10;

% exact solution, using a fine grid
t = a:.0001:b;
y = (1./(19.*t)) - (524288./(19.*(t.^20))); % this is a vector of values, not a function

% coarse solution
h = .01;
ya = 0;
[T1,Y1]=euler(f,a,b,ya,h);

% fine solution
h = .001;
ya = 0;
[T2,Y2]=euler(f,a,b,ya,h);

% finer solution
h = .0001;
ya = 0;
[T3,Y3]=euler(f,a,b,ya,h);

plot(t,y,'k',T1,Y1,'bo-',T2,Y2,'ro-',T3,Y3,'go-')
legend('Exact','h=0.01','h=0.001','h=0.001')
title('The Euler Method with 3 meshes')

Answer 1

[Geoff Hayes]

Kaylene - if I run your code, I notice that your Y array output from euler are all NaNs. Looking closely at this function

 function[T,Y] = euler(f,a,b,ya,h)
 a = 0; b = 1;
 T = a:h:b;
 Y = zeros(1,length(T));
 Y(2) = ya;
 for k = 1 : length(T)-1
      Y(k+1) = Y(k) + h*f(T(k),Y(k));
 end

the a and b inputs are overwritten with 0 and 1 respectively. Why? If I remove these initializations and change the initial value for Y (so Y(1) and not Y(2)) then the code becomes

 function[T,Y] = euler(f,a,b,ya,h)
 T = a:h:b;
 Y = zeros(1,length(T));
 Y(1) = ya;
 for k = 1 : length(T)-1
      Y(k+1) = Y(k) + h*f(T(k),Y(k));
 end

which (at least) initializes Y to be something that can be drawn to your figure. The output using the different step sizes appears to be near identical which may not be what you are trying to show.