Second order diffrential equation solve using ode 45

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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
---------------------------------------------
main program
---------------------------------------------
t=linspace(0,500,1000); %time span%
y0=[0];
%%solving using ode45
[tsol, ysol]=ode45(@(t,y0) firstodefun2(t,y0), t, y0);
---------------------------------------------------
function definition
----------------------------------------------------
function dy=firstodefun2(t,y0)
dy=zeros(1,1);
dy(1)=sin(100*t)-y0(1);
end

Accepted Answer

Sam Chak
Sam Chak on 22 Aug 2022
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

More Answers (1)

Torsten
Torsten on 22 Aug 2022
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).

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