Using euler's method to plot x(t) graph

I created a code to run euler's method for the function x^3+x^2-12x. It works and everything seems to be fine, but when I try to create the x(t) graph using euler's method it does not graph the anticipated graph. The anticipated graph is the hand-drawn graph. The graph I receive is based on the codes I provided. I'm not sure where my code is maybe producing incorrect values in order to get the hand-drawn graph.

function y = eulersub(a,b)

h = 0.01;

x = -5:h:5;

y = zeros(size(x));

y(1)=-40;

n = numel(y);

for i=1:n-1

f = 3*x(i).^2+2*x(i)-12;

y(i+1) = y(i) + h * f;

end

plot(x,y)

ICs = zeros(4,1);

ICs(1) = -5;

ICs(2) = -2;

ICs(3) = 2;

ICs(4) = 5;

timeVector = linspace(0,15,1001);

vecSize = size(timeVector);

outputValues = zeros(vecSize(1));

hold on

for z=1:4

outputValues = eulersub(ICs(z), timeVector);

plot(outputValues, timeVector)

end

hold off

Answer 1

[Torsten]

You pass "ICs(z)" and "timeVector" to "eulersub". In the function, they get the names a and b. But a and b are never referenced in "eulersub". So for all initial conditions you pass to the function, you work with y(0) = -40 and a time interval between -5 and 5.

Maybe you mean

ICs = zeros(4,1);
ICs(1) = -5;
ICs(2) = -2;
ICs(3) = 2;
ICs(4) = 5;
timeVector = linspace(0,15,1001);
vecSize = numel(timeVector);
outputValues = zeros(4,vecSize);
for z=1:4
    outputValues(z,:) = eulersub(ICs(z), timeVector);
end 
plot(timeVector,outputValues)

function y = eulersub(y0,timeVector)
  x=timeVector;
  y = zeros(size(x));
  y(1)=y0;
  n = numel(y);
  for i=1:n-1
    f = 3*x(i).^2+2*x(i)-12;
    y(i+1) = y(i) + (x(i+1)-x(i)) * f;
  end
end