simple second order ODE solver

Hello, I am trying to solve this second order ODE.

(d^2(x)/dt^2)+(dx/dt)+x=0

x(0)=0,x'(0)=1

t=[0 10]

I have tried using ODE 45 and dsolve , however when I always get some kind of error message either regarding my t input or my x''. If anyone has can lend assistance that would be much appreciated. Thanks in advance.

[Jan]

Please post your code and the a copy of the complete error message. Then suggesting an improvement is easier and you can learn what went wrong.

Answer 1

[Torsten]

You can't prescribe x''(0) for a 2nd order ODE.

Best wishes

Torsten.

[Derek Bindbeutel]

Oh sorry its actually x'(0)=1

[Torsten]

syms y(t)
Dy = diff(y);
dsolve(diff(y, 2) + diff(y) + y == 0, y(0) == 0, Dy(0) == 1)

Best wishes

Torsten.

[Derek Bindbeutel]

Thanks this is a lot of help. How will add a time span from 0 to 10 t=[0,10] affect this method?

[Torsten]

No. t will be a variable in the answer.

Solution is here:

http://www.wolframalpha.com/input/?i=y''+%2B+y'+%2B+y+%3D+0,+y(0)%3D0,+y'(0)%3D1

Best wishes

Torsten.

Answer 2

[Jan]

function yourIntegration
x0 = [0; 1];
[t, x] = ode45(@YourODE, x0, [0, 10]);
plot(t, x);

function dx = YourODE(t, x)
dx = [x(2) ; ...
      -x(2) - x(1)];