For those problem i factor the differential operator using t

For those problem (i) factor the differential operator using the Matlab roots() command, (ii) obtain the general solution with the four free constants, and (iii) indicate whether Y (T) is stable or unstable. Suppose you were told that the general solution for a problem was What is the original differential equation associated with this general solution? (Suggest you start by writing the differential operator associated with each fundamental solution and multiply them together) Suppose the problem also requires that: Use matlab to determine the values of A, B, C, and E using the above boundary conditions so that you can plot the y(t) on 0 lessthanorequalto t lessthanorequalto lessthanorequalto 5, From your answer to part (b), determine: y(1) y(2) y(3), and y(4)

Solution

e = \'D4y +4*D3y +5*Dy+2*y=4*t\';
%i = \'y(0)=2, Dy(0)=3\';
y=dsolve(e,\'t\');

e2 = \'D4y +6*D3y +9*Dy=4*t\';
%i = \'y(0)=2, Dy(0)=3\';
y2=dsolve(e2,\'t\');

e3 = \'D4y +6*D3y +16*D2y=4*t\';
%i = \'y(0)=2, Dy(0)=3\';
y3=dsolve(e3,\'t\');

e4 = \'D4y +16*y=4*t\';
%i = \'y(0)=2, Dy(0)=3\';
y4=dsolve(e4,\'t\');

%plot(t,z);
%x = linspace(0,1,7);

%t=(0:1:7);
%z = eval(vectorize(y));%vectorize convert object into string
%plot(t,z);