Matlab - Equaciones diferenciales ODE MATLAB

>> clear all

syms  y(x)

Dy = diff(y,1);

y=dsolve(diff(y, 2) +8*Dy+8*y== sin(x), y(0) == 1, Dy(0) == 0)

y =

(2^(1/2)*exp(-x*(2*2^(1/2) + 4))*exp(4*x + 2*2^(1/2)*x)*(cos(x) - sin(x)*(2*2^(1/2) + 4)))/(8*((2*2^(1/2) + 4)^2 + 1)) - (exp(x*(2*2^(1/2) - 4))*(19669*2^(1/2) + 27364))/(8*(16*2^(1/2) - 25)*(16*2^(1/2) + 25)^2) - (2^(1/2)*exp(x*(2*2^(1/2) - 4))*exp(4*x - 2*2^(1/2)*x)*(cos(x) + sin(x)*(2*2^(1/2) - 4)))/(8*((2*2^(1/2) - 4)^2 + 1)) - (2^(1/2)*exp(-x*(2*2^(1/2) + 4))*(14*2^(1/2) + 37))/(8*(16*2^(1/2) + 25))

function ode45ecuaciones2

% u1=y   --->  u1'=y'=u2

% u2=y' ---> u2'=y''=sin(x)-8*u1-4*u2

% y(0)=1   ---->u1(0)=y(0)=1

% y'(0)=0  ----u2(0)=y'(0)=0

options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);

[T,Y] = ode45(@ecuaciones,[0 12],[0 1],options);

plot(T,Y(:,1),'-',T,Y(:,2),'-.')

function du = ecuaciones(x,u)

du = zeros(2,1);    % a column vector

du(1) = u(2);

du(2) = sin(x)-8*u(1)-4*u(2);