Internal
problem
ID
[8571]
Book
:
Second
order
enumerated
odes
Section
:
section
2
Problem
number
:
36
Date
solved
:
Sunday, November 10, 2024 at 09:12:32 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
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 -> trying 2nd order, dynamical_symmetries, fully reducible to Abel through one integrating factor of the form G(x,y)/(1+H(x,y)*y)^2 --- trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for dynamical symmetries --- -> trying 2nd order, dynamical_symmetries, fully reducible to Abel through one integrating factor of the form G(x,y)/(1+H(x,y)*y) trying 2nd order, integrating factors of the form mu(x,y)/(y)^n, only the singular cases trying symmetries linear in x and y(x) <- linear symmetries successful`
Solving time : 0.057
(sec)
Leaf size : 22
dsolve(x^2*diff(diff(y(x),x),x)+(diff(y(x),x)*x-y(x))^2 = 0, y(x),singsol=all)