Find Coefficients of a 5th order ODE without ode45

The code below I came up with, I am getting the correct roots but the constants are wrong and the graph is not correct either. Can you please help me figure out why it's coming out incorrect.

%Eqn: y'''''-5y'''+4y' = 0

format long
Coefa = 1;
Coefb = 0;
Coefc = -5;
Coefd = 0;
Coefe = 4;
Coeff = 0;
x0 = 0; Yin = 3, Yder1 = -5, Yder2 = 11 , Yder3 = -23, Yder4 = 47,

Yin = 
     3

Yder1 = 
    -5

Yder2 = 
    11

Yder3 = 
   -23

Yder4 = 
    47

B = [Yin Yder1  Yder2 , Yder3 Yder4]; N = 1000;
x = linspace(0,25,N);
y = zeros(1,N);
R = zeros(1,4); 
R = SecondOderODE1(Coefa,Coefb, Coefc,Coefd, Coefe,Coeff);

Unrecognized function or variable 'SecondOderODE1'.

if abs(R(1)-R(4))>=1/10^6
    A = [exp(R(1).*x0), exp(R(2).*x0), exp(R(3).*x0), exp(R(4).*x0), exp(R(5).*x0); exp(x0.*R(1)).*R(1), R(2).*exp(x0.*R(2)), exp(x0.*R(3)).*R(3), exp(x0.*R(4)).*R(4), exp(x0.*R(5)).*R(5)];
    C = B./A
    for i = 1:1:N
        y(i) = real(C(1)*exp(R(1)*x(i)) + C(2)*exp(R(2)*x(i)))+ C(3)*exp(R(3)*x(i))+ C(4)*exp(R(4)*x(i))+ C(5)*exp(R(5)*x(i));
        figure(1)
        plot (x,y)
        xlabel ('x')
        ylabel('y')
        grid on
    end
end
figure(1)
plot(x,y)
xlabel ('x')
ylabel('y')
grid on 

Answer 1

[Torsten]

syms t x(t)
Dx = diff(x,t);
D2x = diff(x,t,2);
D3x = diff(x,t,3);
D4x = diff(x,t,4);
D5x = diff(x,t,5);
eqn = D5x-5*D3x+4*Dx == 0;
conds = [x(0) == 3,Dx(0) == -5,D2x(0) ==11, D3x(0) == -23, D4x(0)==47];
sol = dsolve(eqn,conds)

sol = 

fplot(sol,[0 1])

[Tashanda Rayne]

I appreciate this code, is there anyway you can help me figure out why my code is not working?

[Torsten]

If you explain how your code is supposed to work: maybe.

What is "SecondOderOde1" ? Do you try to determine the roots of the characteristic polynomial of your ODE, thus the zeros of x^5-5*x^3+4*x = 0 ?

[Tashanda Rayne]

% "SecondOderOde1"

function [R] = SecondOderODE1(Coefa, Coefb, Coefc, Coefd, Coefe, Coeff);

p = zeros(1,6); R = zeros(1,6);

p = [Coefa, Coefb, Coefc, Coefd, Coefe, Coeff];

R = roots(p);

end

The code is supposed to solve for roots and constants. I got it to solve for the roots but when trying to solve for the constants it is returning my I.C. I am attempting to solve this problem without using ODE45 or dsolve

[Torsten]

The roots could be complex-valued or a root could be of higher order than 1. How do you handle this with your code ?

In short: a solution without dsolve or ODE45 will get much more complex than the code you posted.

For the equation posted, a paper-and-pencil solution will be easiest - and it doesn't use ODE45 or dsolve :-)