Internal
problem
ID
[8306]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
3.0
Problem
number
:
22
Date
solved
:
Sunday, November 10, 2024 at 09:09:44 PM
CAS
classification
:
[[_2nd_order, _missing_y]]
Solve
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) trying differential order: 2; missing variables `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = exp_sym -> Calling odsolve with the ODE`, diff(_b(_a), _a) = -(_b(_a)^2-_a+1)/(_a^2+1), _b(_a)` *** Sublevel 2 *** Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear trying Bernoulli trying separable trying inverse linear trying homogeneous types: trying Chini differential order: 1; looking for linear symmetries trying exact Looking for potential symmetries trying Riccati trying Riccati sub-methods: <- Abel AIR successful: ODE belongs to the 2F1 2-parameter class <- differential order: 2; canonical coordinates successful <- differential order 2; missing variables successful`
Solving time : 0.021
(sec)
Leaf size : 377
dsolve((x^2+1)*diff(diff(y(x),x),x)+1+diff(y(x),x)^2 = x, y(x),singsol=all)