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
tspan=[1 4]; IC=[0;1;3];
[t,y]=ode23(hw5, tspan, IC);
