help solving a differential equation

Hey guys.

I want to solve differential equation that is connected to a pysical problem. The gist of it is that the position of a ball is 0 at 0 second. The velocity is v0 when t=0. The equation is : x''-x*ω^2=0. My problem is, that I don't know, how could I force matlab to write ω instead of any number?

Thank you in advance!

Answer 1

[Walter Roberson]

>> syms x(t) omega
>> dx = diff(x)
 
dx(t) =
 
diff(x(t), t)
 
>> d2x = diff(dx)
 
d2x(t) =
 
diff(x(t), t, t)
 
>> eqn = d2x - dx*omega^2 == 0
 
eqn(t) =
 
- diff(x(t), t)*omega^2 + diff(x(t), t, t) == 0
 
>> dsolve(eqn)
 
ans =
 
C1 + C2*exp(omega^2*t)
 
>> dsolve(eqn, dx(0) == 0, x(0) == 0)
 
ans =
 
0

Yup. Without initial velocity, the ball just stays where it is.