help solving a differential equation

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Sipka Gergö
Sipka Gergö 2019-11-15
回答： Walter Roberson 2019-11-15
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!

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回答（1 个）

Walter Roberson
Walter Roberson 2019-11-15
>> 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.

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