Matlab - EDO de segundo orden

syms y(t) t

Dy=diff(y, t);

D2y=diff(y, t, 2);

fprintf('To solve: A*ddy+B*dy+C*y=D at ICs: y(0)=a, dy(0)=b \n')

fprintf('Enter the values of [A, B, C, D] and [a, b] \n');

A = input('Enter A = ');

B = input('Enter B = ');

C = input('Enter C = ');

D = input('Enter D = ');

a = input('Enter a = ');

b = input('Enter b = ');

% Given ODE equation:

Equation = D2y==(1/A)*(D - B*Dy-C*y);

ICs = [y(0)==a; Dy(0)==b];

Solution=dsolve(Equation, ICs);

% Display the computed anaytical solution in the command window:

pretty(Solution)

fplot(Solution, [0, 5], 'b-'), grid on

xlabel('\it t')

ylabel('\it Solution, y(t) ')

title('\it Solution of: $$\frac{A*d^2y}{dt^2}+\frac{B*dy}{dt}+C*y=D,y(0)=a, dy(0)=b$$', 'interpreter', 'latex')

if isnumeric(D)

    gtext(['\it A = ' num2str(A), '\it, B = ' num2str(B), '\it, C = ' num2str(C), '\it, D = ' num2str(D)])

else

    gtext(['\it A = ' num2str(A), '\it, B = ' num2str(B), '\it, C = ' num2str(C), '\it, D = ' char(D)])

end

gtext(['\it Initial Conditions: a = ' num2str(a), '\it, b = ' num2str(b)])

grid on; shg

>> ecuacion_diferencial_de_2do_orden

To solve: A*ddy+B*dy+C*y=D at ICs: y(0)=a, dy(0)=b

Enter the values of [A, B, C, D] and [a, b]

Enter A = 1

Enter B = 2

Enter C = -8

Enter D = 2*exp(-2*t)+exp(-t)

Enter a = 1

Enter b = 0

exp(2 t) 29   exp(-4 t) 5   exp(-2 t) (2 exp(t) + 3)   exp(-2 t) (exp(t) + 3)

----------- + ----------- - ------------------------ - ----------------------

     36            9                   36                        18

>> latex_ecuacion_diferencial_de_2do_orden_11_01_22

To solve: A*ddy+B*dy+C*y=D at ICs: y(0)=a, dy(0)=b

Enter the values of [A, B, C, D] and [a, b]

Enter A = 1.3

Enter B = 1

Enter C = 2

Enter D = 3

Enter a = 1

Enter b = 0

                 /   5 t \    / sqrt(235) t \      /   5 t \    / sqrt(235) t \

    sqrt(235) exp| - --- | sin| ----------- |   exp| - --- | cos| ----------- |

3                \    13 /    \      13     /      \    13 /    \      13     /

- - ----------------------------------------- - -------------------------------

2                       94                                     2