Not enough input arguments error in ode23?

I try to use ode23 solver to my 3rd order ODE function. The function is given above.The range of t is from 1 to 4 .

The syntax that i must use is [t, y]= solver(@odefun, tspan, y0)

I also have initial conditions, but i confused where should i put them in the syntax.

Initial conditions are y(1)=0, y'(1)=1 and y''(1)=3.

function yprime = ydotfunc(t,y)

yprime(1)=y(2);

yprime(2)=5*(t^3)*exp(t)+9*(t^3)-3*t*y(2)+4*y(1);

yprime(3)=5*(t^3)*exp(t)+9*(t^3)+(t^2)*y(3)-3*t*y(2)+4*y(1);

end

clc

close all hidden

format long

tspan=[1 4];

IC=[1;1;-1];

[t,u]=ode23(@ydotfunc,tspan,IC);

y_true=@(t) -(t.^2)+t.*cos(log(t))+t.*sin(log(t))+(t.^3).*log(t);

y1=y_true(t);

figure(1)

plot(t,y(:,1),'ro',t,y1,'b-')

title('Plot of y1')

xlabel('t')

ylabel('y1')

legend('Numerical Solution','Exact Solution')

Answer 1

[Star Strider]

Most of what you are doing appears to be correct (I removed the clc and close calls):

tspan=[1 4];
IC=[1;1;-1];
[t,y]=ode23(@ydotfunc,tspan,IC);

y_true=@(t)  -(t.^2)+t.*cos(log(t))+t.*sin(log(t))+(t.^3).*log(t);
y1=y_true(t);
figure(1)
plot(t,y(:,1),'ro',t,y1,'b-')
title('Plot of y1')
xlabel('t')
ylabel('y1')
legend('Numerical Solution','Exact Solution')

The Symbolic Math Toolbox odeToVectorField function disagrees with your coding of your differential equation, and gives a result closer to the exact solution.