Internal
problem
ID
[8379]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
4.0
Problem
number
:
61
Date
solved
:
Sunday, November 10, 2024 at 09:12:27 PM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
Solve
`Methods for second order ODEs: --- Trying classification methods --- trying a quadrature trying high order exact linear fully integrable trying differential order: 2; linear nonhomogeneous with symmetry [0,1] trying a double symmetry of the form [xi=0, eta=F(x)] -> Try solving first the homogeneous part of the ODE checking if the LODE has constant coefficients checking if the LODE is of Euler type trying a symmetry of the form [xi=0, eta=F(x)] checking if the LODE is missing y -> Trying a Liouvillian solution using Kovacics algorithm <- No Liouvillian solutions exists -> Trying a solution in terms of special functions: -> Bessel -> elliptic -> Legendre <- Kummer successful <- special function solution successful <- solving first the homogeneous part of the ODE successful`
Solving time : 0.056
(sec)
Leaf size : 167
dsolve(x/(1-x)*diff(diff(y(x),x),x)+y(x) = 1/(1-x), y(x),singsol=all)
Solving time : 0.248
(sec)
Leaf size : 136
DSolve[{x/(1-x)*D[y[x],{x,2}]+y[x]==1/(1-x),{}}, y[x],x,IncludeSingularSolutions->True]