Second order diffrential equation solve using ode 45

I want to solve a second order differential equation of the form

d^2y/dt^2+dy/dt=sin(100t)

I want the value of dy/dt and y.

I am copied my code below where easily I can get the dy/dt as a function of t but I am not able find y as a function of t. I am new to Matlab. Please help me regarding this issue. I copied the code below

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main program

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t=linspace(0,500,1000); %time span%

y0=[0];

%%solving using ode45

[tsol, ysol]=ode45(@(t,y0) firstodefun2(t,y0), t, y0);

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function definition

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function dy=firstodefun2(t,y0)

dy=zeros(1,1);

dy(1)=sin(100*t)-y0(1);

end

Answer 1

[Sam Chak]

Hi @Abhik Saha

The code is fixed below. This is a 2nd-order system, and so there are two state variables and two initial values.

t  = [0, 10];
y0 = [0 0]; 

% solving using ode45
[tsol, ysol] = ode45(@(t, y) firstodefun2(t, y), t, y0);
plot(tsol, ysol(:, 1)), grid on, xlabel('t, [sec]'), ylabel('y(t)')

function dy  = firstodefun2(t, y)
       dy    = zeros(2, 1);
       dy(1) = y(2);
       dy(2) = sin(100*t) - y(2);
end

[Abhik Saha]

Thanks. it works

Answer 2

[Torsten]

Set x(1) = y and x(2) = dy/dt.

Then you get a system of differential equations

dx(1)/dt = x(2)
dx(2)/dt = -x(2) + sin(100*t)

Of course, you also will have to supply two initial conditions (one for y, the second for dy/dt at t=0).