Solving a third order ODE in MATLAB

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

Answer 1

[Karan Gill]

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.

[Sergio Manzetti]

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]

What do you mean by "other methods"?

Answer 2

[Sergio Manzetti]

Wolfram alpha, it solves it without any problems.

[Sergio Manzetti]

Thanks

[Karan Gill]

Is this what you tried? Didn't work for me.

https://www.wolframalpha.com/input/?i=a*y%27%27%27+-0.5*x%5E2*y+%3D%3D+(abs(y)),+y(0)+%3D+1,+y%27(0)%3D0,+y%27%27(0)%3D0

Could you post your input to Wolfram?

Answer 3

[Sergio Manzetti]

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.

[Torsten]

You used

eqn = a.*D3Y -0.5*x^2*Y == Y

instead of

eqn = a.*D3Y -0.5*x^2*Y == abs(Y)

Best wishes

Torsten.

[Karan Gill]

Thanks for catching that. I also noticed the third condition is different.

[Torsten]

... and I'm surprised that the solution does not depend on "a".

Answer 4

[Sergio Manzetti]

It doesn't matter, abs(Y) did not yield results with either methods, while the former, Y, yielded result only in wolfram.

[Karan Gill]

Thanks for the clarifications. I'll investigate. Note that cond3 is different in your two codes.

[Sergio Manzetti]

Yes, I am aware of that.

Torsten, are there alternative ways to solve:

D3y - x^2y = ay, where a is some constant?