Internal
problem
ID
[8190]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
1.0
Problem
number
:
52
Date
solved
:
Sunday, November 10, 2024 at 09:04:53 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
Solve
`Methods for second order ODEs: --- Trying classification methods --- trying a symmetry of the form [xi=0, eta=F(x)] checking if the LODE is missing y -> 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 changes of variables to rationalize or make the ODE simpler <- unable to find a useful change of variables trying a symmetry of the form [xi=0, eta=F(x)] trying 2nd order exact linear trying symmetries linear in x and y(x) trying to convert to a linear ODE with constant coefficients <- to_const_coeffs successful: conversion to a linear ODE with constant coefficients was determined`
Solving time : 0.056
(sec)
Leaf size : 80
dsolve(diff(diff(y(t),t),t)+(t^2-1)/t*diff(y(t),t)+t^2/(1+exp(1/2*t^2))^2*y(t) = 0, y(t),singsol=all)
Solving time : 0.141
(sec)
Leaf size : 72
DSolve[{D[y[t],{t,2}]+(t^2-1)/t*D[y[t],t]+t^2/(1 + Exp[t^2/2])^2*y[t]==0,{}}, y[t],t,IncludeSingularSolutions->True]