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Solving a third order ODE in MATLAB

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Hi, MATLAB is quite about this command:
syms a h Y(x) g x B E T
D3Y = diff(Y, 3)
eqn = a.*D3Y -0.5*x^2*Y == (abs(Y))
D2Y = diff(Y, 2)
DY = diff(Y)
cond1 = Y(0) == 1;
cond2 = DY(0) == 0;
cond3 = D2Y(0) == 0
Y(x) = dsolve(eqn, cond1, cond2, cond3)
latex(Y(x))
Is there a limit here for solving it? Thanks

Risposta accettata

Karan Gill
Karan Gill il 12 Feb 2018
Do you not get this warning? If you got it, was the warning clear?
Warning: Unable to find explicit solution.
> In dsolve (line 201)
Y(x) =
[ empty sym ]
Try solving numerically using ode45 or similar.
  2 Commenti
Sergio Manzetti
Sergio Manzetti il 13 Feb 2018
Yes I did, but I was surprised, because it is readily solved using other methods. I will check out ode45, however I am not sure it will give an analytical solution.
Karan Gill
Karan Gill il 13 Feb 2018
What do you mean by "other methods"?

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Più risposte (3)

Sergio Manzetti
Sergio Manzetti il 14 Feb 2018
Wolfram alpha, it solves it without any problems.

Sergio Manzetti
Sergio Manzetti il 15 Feb 2018
Modificato: Sergio Manzetti il 15 Feb 2018
I tried this on wolfram, which is the equivalent of this:
syms a h Y(x) g x B E T
D3Y = diff(Y, 3)
eqn = a.*D3Y -0.5*x^2*Y == Y
D2Y = diff(Y, 2)
DY = diff(Y)
cond1 = Y(0) == 1;
cond2 = DY(0) == 0;
cond3 = D2Y(0) == 1;
Y(x) = dsolve(eqn, cond1, cond2, cond3)
latex(Y(x))
and I got a result,Z = 1/3*(exp(x) + 2*exp(-x/2)*cos((sqrt(3)*x)/2)) , however, the result is now non-visible because of std computation time exceeded.
  3 Commenti
Karan Gill
Karan Gill il 15 Feb 2018
Thanks for catching that. I also noticed the third condition is different.
Torsten
Torsten il 15 Feb 2018
... and I'm surprised that the solution does not depend on "a".

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Sergio Manzetti
Sergio Manzetti il 15 Feb 2018
It doesn't matter, abs(Y) did not yield results with either methods, while the former, Y, yielded result only in wolfram.
  2 Commenti
Karan Gill
Karan Gill il 15 Feb 2018
Thanks for the clarifications. I'll investigate. Note that cond3 is different in your two codes.
Sergio Manzetti
Sergio Manzetti il 15 Feb 2018
Modificato: Sergio Manzetti il 15 Feb 2018
Yes, I am aware of that.
Torsten, are there alternative ways to solve:
D3y - x^2y = ay, where a is some constant?

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