MATLAB: Fourth order differential equation

Question

syms f(x)

Df = diff(f,x);

D2f = diff(f,x,2);

D3f = diff(f,x,3);

D4f = diff(f,x,4);

ode =3*D4f+(2*x^2+6)*D3f+5*D2f-Df-2*f == – 4*x^6+ 2*x^5 -55*x^4 – 24*x^3 – 22*x^2 – x*32;

cond1 = f(0)==0;

cond2 = Df(0)==1;

cond3 = D2f(0) == -8;

cond4 = D3f(0) == 6;

conds = [cond1 cond2 cond3 cond4];

fSol(x) = dsolve(ode,conds);

figure

ezplot(fSol(x),[0 1])

The error is :

Warning: Unable to find explicit solution.

> In dsolve (line 201)

(line 13)

Error using inlineeval (line 14)

Error in inline expression ==> matrix([])

Undefined function 'matrix' for input arguments of type 'double'.

Error in inline/feval (line 33)

INLINE_OUT_ = inlineeval(INLINE_INPUTS_, INLINE_OBJ_.inputExpr, INLINE_OBJ_.expr);

Error in ezplotfeval (line 51)

z = feval(f,x(1));

Error in ezplot>ezplot1 (line 486)

[y, f, loopflag] = ezplotfeval(f, x);

Error in ezplot (line 158)

[hp, cax] = ezplot1(cax, f{1}, vars, labels, args{:});

Error in sym/ezplot (line 78)

h = ezplot(fhandle(f),varargin{:});%#ok<EZPLT>

Error in try2 (line 15)

ezplot(fSol(x),[0 1])

Answer 1

If an analytical solution is not an option, and a plot of the solution is the objectrive:

syms f(x) X Y 
Df = diff(f,x);
D2f = diff(f,x,2);
D3f = diff(f,x,3);
D4f = diff(f,x,4);
ode =3*D4f+(2*x^2+6)*D3f+5*D2f-Df-2*f == - 4*x^6+ 2*x^5 -55*x^4 - 24*x^3 - 22*x^2 - x*32;
% cond1 = f(0)==0;
% cond2 = Df(0)==1;
% cond3 = D2f(0) == -8;
% cond4 = D3f(0) == 6;
[VF,Sbs] = odeToVectorField(ode);
odefcn = matlabFunction(VF, 'Vars',{x,Y});
[X,Y] = ode45(odefcn, [0 1], [0 1 -8 6]);
figure
plot(X, Y)
grid
legend(string(Sbs))
producing: