4th order ODE, 4 boundary conditions

I have a 4th order ODE, with 4 boundary conditions.

The ODE problem is

y''''(x) = y(x)*y'''(x) - y'(x)*y''(x)

With the 4 boundary conditions:

y(0) = 0.1, y(1) = 0, y'(0) = 0, y'(1) = 0.

I started off my code by writing the ODE as a system of first order ODE's,

function dydx = ab(x,y)

dydx = zeros(4,1);

dydx(1) = y(2);

dydx(2) = y(3);

dydx(3) = y(4);

dydx(4) = y(1)*y(4) - y(2)*y(3);

Then defining the 4 boundary conditions,

function res = bc4(ya,yb)

res = [ya(1)-0.1; yb(1); ya(2); yb(2)];

Followed by:

solinit = bvpinit(linspace(0,0.05,1), [1, 0]);

sol = bvp4c(@ab, @bc4,solinit);

x = linspace(0,1);

y = deval(sol.x);

plot(x,y(1,:));

However, I already get an error on the second line,

"Not enough input arguements. Erron in __ (line 3)

dydx = y(2)"

Any ideas on what is going wrong?

Answer 1

[Torsten]

%solinit = bvpinit(linspace(0,0.05,1), [1, 0]);
solinit = bvpinit(0:0.05:1, [1, 0,0,0]);
sol = bvp4c(@ab, @bc4,solinit);
%x = linspace(0,1);
%y = deval(sol.x);
%plot(x,y(1,:));
plot(sol.x,[sol.y(1,:);sol.y(2,:)]);

function dydx = ab(x,y)
  dydx = zeros(4,1);
  dydx(1) = y(2);
  dydx(2) = y(3);
  dydx(3) = y(4);
  dydx(4) = y(1)*y(4) - y(2)*y(3);
end

function res = bc4(ya,yb)
  res = [ya(1)-0.1; yb(1); ya(2); yb(2)];
end

Answer 2

[MOSLI KARIM]

%%

function answer_matlab 
clc
clear all
close all
format long 

mesh=20;
 x=linspace(0,1,mesh)
solinit=bvpinit(linspace(0,1,10),[0.1 ;0 ;0; 0])
sol=bvp4c(@fct,@bc,solinit)
y=deval(sol,x)
figure(1)
hold on 
plot(x,y(1,:))

function dxdy=fct(x,y)

dxdy=[y(2);y(3);y(4);y(1)*y(4)-y(2)*y(3) ];


end 

function res=bc(ya,yb)

res=[ya(1)-0.1
     yb(1)
     ya(2)
     yb(2)
     
     ];
end 
end