Solving 4th Order Differential Equations

I am trying to solve a fourth order Differential Equation (no previous Diff Q experience) and I'm running into issues with the ode45 function. I think I have entered the differential equations correctly in order for MATLAB to see them as first order equations. Any help is welcome. The equation would be f = f2 below.

if true
  %clear all
clc

t = [0 9]; syms y y0

yx = y^3; y1 = diff(y0,1);

y2 = diff(y0,2);

y3 = diff(y0,3);

y4 = diff(y0,4);

f=y4+5.*(1-y0)*y3+2.*y2+3*y1+yx;

f2 = 10.*sin(pi.*t);

z = [y0 y1 y2 y3]; Z = transpose(z);

y0=0; [t,y] = ode45(@(z,y)f2,t,y0); end

[John D'Errico]

Please don't put in comments as an answer. And then don't accept your own answer.

I moved your accepted answer into a comment. Please accept Star's answer if you feel it helped you.

Answer 1

[Star Strider]

You appear to be on the correct path.

I would take your original symbolic differential equation as an argument to the Symbolic Math Toolbox odeToVectorField (link) function, then use that output to an argument to the matlabFunction (link) function:

syms y(t) y0(t) Y t 

yx = y^3; 
y1 = diff(y0,1);
y2 = diff(y0,2);
y3 = diff(y0,3);
y4 = diff(y0,4);

f=y4+5.*(1-y0)*y3+2.*y2+3*y1+yx;

[F, Fsubs] = odeToVectorField(f)
Fcn = matlabFunction(F, 'Vars',{t Y})

This gives you:

F =

                                           Y[2]
                                           Y[3]
                                           Y[4]
   (5*Y[1] - 5)*Y[4] - y(t)^3 - 3*Y[2] - 2*Y[3]

Fsubs =

     y0
    Dy0
   D2y0
   D3y0

and (slightly edited):

Fcn = @(t,Y) [Y(2); Y(3); Y(4); -y(t).^3+(Y(1).*5.0-5.0).*Y(4)-Y(2).*3.0-Y(3).*2.0];

that you can use in ode45.

[Star Strider]

My pleasure!

[John D'Errico]

Moving the "non-answer" comment into a comment from Michael:

"Thanks! That was a great help!"