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How to solve differential equation of series general solution

21 vues (au cours des 30 derniers jours)
J
J le 14 Mar 2023
Commenté : J le 14 Mar 2023
How do we solve differential equation of series general solution?
For example, I tried to solve this differential equation into series solution, but as you can see in the result, it is not showing like y = C1 x^(1/4)(1 - (1/14)x + (1/616)x^2 + ...) + C2 x^(-1/2) (1 - (1/2)x + (1/40)x^2 + ...) and this is the series general solution that I want to make for the result.
How can make the result in the photo to the form like how I typed right before? Could you please type the command for the solution clearly? Thank you :)
  1 commentaire
John D'Errico
John D'Errico le 14 Mar 2023
Please do not paste in a picture of your code. Then we need to type in the code by hand. Had you simply pasted in text, then we could more easily help you. Is there a good reason why you want to make it more difficult to get help?

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Réponses (1)

John D'Errico
John D'Errico le 14 Mar 2023
Assuming I typed in that line correctly...
syms y(x)
S = dsolve(8*x^2*diff(y,2)+10*x*diff(y)+(x-1)*y==0,'ExpansionPoint',0, 'Order',8)
S = 
There were TWO independent solutions found. You have TWO unknown conditions, which are typically supplied as boundary or initial conditions. But consider what this does?
syms C1 C2
C1*S(1) + C2*S(2)
ans = 
  5 commentaires
John D'Errico
John D'Errico le 14 Mar 2023
Modifié(e) : John D'Errico le 14 Mar 2023
I believe there is no specific tool to do exactly that.
J
J le 14 Mar 2023
Aha I see Thank you!
Is is correct that 'ExpansionPoint',0 represents that the center is 0 which means x naught = 0 and it is correct that 'Order', 8 means the solution terms are 8 terms?

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