Coding a solution to a second order ODE with ode45 or simulink

Please help! y''+by'+siny=0 -Plot the numerical solution of this differential equation with initial conditions y(0)=0, y'(0)=4, from t=0 to t=20 -Do the same for the linear approximation y''+by'+y=0 -Compare linear and nonlinear behavior for values b = 1, 1.5, 2

[madhan ravi]

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[Alex Patterson]

syms t f

function fprime = pendulum(t, f) b = [1, 1.5, 2]; fprime = zeros(size(f)); fprime(1) = f(2); fprime(2) = -sin(f(1))-b*f(2); [t f] = ode45('pendulum', [0 20], [0 4]); plot(t,f(:,1)) end

Answer 1

[madhan ravi]

[t,f] = ode45(@pendulum, [0 20], [0 4]); % calling of the function

plot(t,f(:,1),'g')
hold on
plot(t,f(:,2),'r')

function fprime = pendulum(t, f) 
    b = 1; % b should be a scalar
    fprime = zeros(size(f)); 
    fprime(1) = f(2); 
    fprime(2) = -sin(f(1))-b*f(2); 
    fprime=[fprime(1);fprime(2)]
end

[madhan ravi]

If something is not clear let know else accept the answer so that people know the question is solved

[Alex Patterson]

Is there a way I can plot a second equation on the same graph? Thank you.

[madhan ravi]

see edited