solve the following nonlinear system with a discret input and compare to the linearization

[poster]

enter image description here Please refer the problem on the attached link. Below is my code, but it doesn't give me the graph I wanted. The correct graph is shown on picture. I am new for matlab and any help is greatly appreciated.

function dydt = mix(t,y,c,d)  % function dydt is dy/dt with input t, y is either height or temperature

                               % y(1) is height, y(2) is temperature

                               % c = qc(t), d = qh(t)



dydt = [1/3*(c+d -(0.7*0.05*(19.6*y(1))^0.5)); 1/(3*y(1))*(c*(10-y(2))+d*(90-y(2)))]; % The first part          % is dy(1)/dt = dh/dt and the second part after the semicolon is dy(2)/dt = dTt/dt.



>>  tspan = linspace(0,100,100);  % tspan from 0 to 100 with 100 steps

dydt = zeros(2,1);  %for dh/dt and dT/dt

c =zeros(100,1);

d = zeros(100,1);

for i = 1:numel(tspan)

    if i<=25

        c(i) = 0.022;  % c is qc(t) in the example

        d(i) = 0.14;   % d is qh(t) in the example

    elseif (25< i)&& (i<=60)

        c(i) =0.043;

        d(i)= 0.14;

    else

        c(i) = 0.043;

        d(i) = 0.105;

    end

    [t,y] = ode45(@(t,y)mix(t,y,c(i),d(i)), tspan, [1.10 81.5]);

    plot(t,y(:,1)) % for height vs time graph

    plot(t,y(:,2))  % Temperature vs time graph

    drawnow;

end

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