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dsolve - Unable to find explicit solution

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Jakub Jedrzejczyk
回答： Om Yadav 2020-4-24
Hi there! I'm trying to solve differetial equation:
Unfortunately result of code:
gamma = 1.4
P0 = 1
Pe = 9.4
R = 0.168
syms S P(t)
eqn = diff(P,t) == (3/R)*S*(Pe-P0)*((P/P0)^(1/gamma))*(1-((P0/P)^(1/gamma))*((Pe-P)/(Pe-P0)))^(2/3);
dsolve(eqn)
is:
Warning: Unable to find explicit solution. Returning implicit solution instead.
> In dsolve (line 208)
In Untitled (line 7)
ans =
1
1/root(z^6 + z^5 + z^4 + z^3 + z^2 + (5*z)/47 + 5/47, z, 1)^7
solve(int(42^(2/3)/(P^(5/7)*(5*P^(2/7) - 47/P^(5/7) + 42)^(2/3)), P, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) - 150*S*t - C11 == 0, P)
What i'm doing wrong?

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采纳的回答

Walter Roberson
Walter Roberson 2018-3-7
Nothing. It just does not have a closed form solution that can reasonably be found.

更多回答（2 个）

Jakub Jedrzejczyk
I want to fit this equation in experimental data. Is it possible to do it by means of Levenberg-Marquardt method?
  8 个评论
显示 6更早的评论
Nenad Vujovic
Nenad Vujovic 2020-1-25
Can someone solve this:
>> syms y(t);
dsolve('Dy=sin(t)*cos(t)+2-(y*cos(t))')
ans =
C5*exp(-sin(t)) + exp(-sin(t))*int((exp(sin(t))*(sin(2*t) + 4))/2, t, 'IgnoreAnalyticConstraints', true)
Walter Roberson
Walter Roberson 2020-1-25
That is the solution. Most integrals do not have closed form solutions.

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Om Yadav
Om Yadav 2020-4-24
We got it very well that closed formula for my problem does not exist. The question is, how to get a numerical solution using dsolve?

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