Internal
problem
ID
[8283]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
2.0
Problem
number
:
52
Date
solved
:
Sunday, November 10, 2024 at 03:34:36 AM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
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 -> hyper3: Equivalence to 1F1 under a power @ Moebius -> hypergeometric -> heuristic approach -> hyper3: Equivalence to 2F1, 1F1 or 0F1 under a power @ Moebius -> Mathieu -> Equivalence to the rational form of Mathieu ODE under a power @ Moebius trying a solution in terms of MeijerG functions -> Heun: Equivalence to the GHE or one of its 4 confluent cases under a power @ Moebius -> trying a solution of the form r0(x) * Y + r1(x) * Y where Y = exp(int(r(x), dx)) * 2F1([a1, a2], [b1], f) trying a symmetry of the form [xi=0, eta=F(x)] trying symmetries linear in x and y(x) trying to convert to a linear ODE with constant coefficients trying 2nd order, integrating factor of the form mu(x,y) trying to convert to an ODE of Bessel type -> trying reduction of order to Riccati --- Trying Lie symmetry methods, 2nd order --- `, `-> Computing symmetries using: way = 3`[0, x+y]
Solving time : 0.290
(sec)
Leaf size : maple_leaf_size
dsolve(diff(diff(y(x),x),x)-diff(y(x),x)*x^3-y(x)*x^3-x^4-x^3 = 0, y(x),singsol=all)