dsolve - Unable to find explicit solution
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Jakub Jedrzejczyk
il 7 Mar 2018
Hi there! I'm trying to solve differetial equation:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/171047/image.jpeg)
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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Risposta accettata
Walter Roberson
il 7 Mar 2018
Nothing. It just does not have a closed form solution that can reasonably be found.
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Più risposte (2)
Jakub Jedrzejczyk
il 7 Mar 2018
8 Commenti
Nenad Vujovic
il 25 Gen 2020
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
il 25 Gen 2020
That is the solution. Most integrals do not have closed form solutions.
Om Yadav
il 24 Apr 2020
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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