Solving a third order ODE in MATLAB

Question

Sergio Manzetti 2018-2-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/381764-solving-a-third-order-ode-in-matlab

编辑： Sergio Manzetti 2018-2-15

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

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Answer 1

Karan Gill 2018-2-12

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https://ww2.mathworks.cn/matlabcentral/answers/381764-solving-a-third-order-ode-in-matlab#answer_304782

在 MATLAB Online 中打开

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.

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Sergio Manzetti 2018-2-13

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 2018-2-13

What do you mean by "other methods"?

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Answer 2

Sergio Manzetti 2018-2-14

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https://ww2.mathworks.cn/matlabcentral/answers/381764-solving-a-third-order-ode-in-matlab#answer_305097

Wolfram alpha, it solves it without any problems.

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Sergio Manzetti 2018-2-14

Thanks

Karan Gill 2018-2-14

编辑：Karan Gill 2018-2-14

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?

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Answer 3

Sergio Manzetti 2018-2-15

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/381764-solving-a-third-order-ode-in-matlab#answer_305293

编辑：Sergio Manzetti 2018-2-15

在 MATLAB Online 中打开

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.