Solve a second order differential equation

Hi, I am completely new to Matlab and am looking to solve a simple second order differential equation:

y''+w^2*y=0 IC: y(0)=0, y'(0)=1 BC=[0,pi]

I am looking to solve for both y(x) and y'(x)

I understand this is a simple equation to solve and have done it fine on paper. However I have been trying different ways to solve it on matlab but to no avail. I have tried both dsolve and ode45 functions but did not quite understand what I was doing. Any help would be great. Thanks in advance, Ben

Answer 1

[Azzi Abdelmalek]

% x1=y
%x2=dy

Then

%dx1=dy=x2
%dx2=d2y=-w^2*y=-w^2*x1

save this function as yourfcn

function dx=yourfcn(t,x)
w=1
dx(1)=x(2)
dx(2)=-w^2*x(1)

Then call the ode45 function

[t,x]=ode45(@yourfcn,[0,pi],[0 0])

Then deduce y

y=x(:,1)

Answer 2

[Shashank Prasanna]

I really recommend going through our documentation and these things become intuitive. Most standard setup's usually have examples in the documentation:

http://www.mathworks.com/help/matlab/math/ordinary-differential-equations.html#brfg9jq-1

[Ben]

Thanks for the help guys. Didn't realise this documentation existed. Very useful. Thanks

Answer 3

[Nicolas]

Hi I have written the following First the Function

function h = goo(t,y)
h = zeros(3,1);    
h(1) = y(2) * y(3);
h(2) = -y(1) * y(3);
h(3) = -0.51 * y(1) * y(2);  
end

and then the code

clear all
initial=[-2 -3.5 21];
time=[0 10];
[t,y] = ode45(@goo,time,initial);
plot (t,y)

However I always get the following message:

Error using feval
Undefined function 'goo' for input arguments of type 'double'.
Error in odearguments (line 88)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.
Error in ode45 (line 114)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Can anyone help me on this Thank you