I need ode 23 help PLEASE

I have a very basic code about ode23 but i can not see my faults.

I must solve 3rd order ODE t^3*y''' - t^2 * y'' + 3 * t * y' - 4*y = 5*t^3 * ln(t) + 9 * t^3 for the interval t [1,4]. I must use ode23 solver and [t,y]=solver(@odefun, tspan, y0). .

exact solution is ye(t) = - t^2 + t*cos(ln(t)) + t*sin(ln(t)) + t^3 * ln(t)

The initial conditions y(1) = 0 , y'(1) = 1 and y''(1) = 3 I want to plot the exact and numerical solution for y together in same figure.

I write some code with get help from internet but i couldn't run it.

I get error.

clc
clear all
close all

function dydt = hw5(t,y)
dydt=zeros(4,1);
dydt(1)=y(2);
dydt(2)=(t*t^(3)*log(t)+9*t^3 + 4 y(1) - 3*t*y(2) - t^3*y(4)) / -t^2;
dydt(3)=y(4);
dydt(4)=(5*t^3*log(t) + 9*t^3 + t^2*y(4) - 3*t*y(3) + 4*k^2 ) / t^3;
end

% Write the main program (i.e. script) as given below.
tspan=[1 4]; IC=[0;1;3];
[t,y]=ode23(hw5, tspan, IC);

[Star Strider]

First, you are missing an operator here:

dydt(2)=(t*t^(3)*log(t)+9*t^3 + 4 y(1) - 3*t*y(2) - t^3*y(4)) / -t^2;
                                 ↑

that I assume is suppossed to be multiplication.

Second, you have 4 equations and 3 initial conditions. You need an extra initial condition.

[hgrlk]

I changed that you said but I get still have

Attempted to access t(0); index must be a positive integer or logical.

error.. I think i have some problems too

[Star Strider]

If you want t=0, you need to address it as t(1).

[hgrlk]

I want to plot the exact and numerical solution for y together in same figure. But I cannot figure out how i can solve my error.