How to solve differential equation of series general solution
10 vues (au cours des 30 derniers jours)
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 :)
John D'Errico le 14 Mar 2023
Assuming I typed in that line correctly...
S = dsolve(8*x^2*diff(y,2)+10*x*diff(y)+(x-1)*y==0,'ExpansionPoint',0, 'Order',8)
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)