Internal
problem
ID
[8202]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
1.0
Problem
number
:
64
Date
solved
:
Sunday, November 10, 2024 at 09:04:54 PM
CAS
classification
:
[[_Emden, _Fowler], [_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 2nd order, integrating factors of the form mu(x,y)/(y)^n, only the singular cases trying symmetries linear in x and y(x) trying differential order: 2; exact nonlinear trying 2nd order, integrating factor of the form mu(y) trying 2nd order, integrating factor of the form mu(x,y) trying 2nd order, integrating factor of the form mu(x,y)/(y)^n, only the general case trying 2nd order, integrating factor of the form mu(y,y) -> Calling odsolve with the ODE`, -(_y1^3-4)*y(x)/_y1^3+2*((diff(y(x), x))*x+_y1)/_y1^3, y(x)` *** Sublevel 2 *** Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful trying differential order: 2; mu polynomial in y trying 2nd order, integrating factor of the form mu(x,y) differential order: 2; looking for linear symmetries differential order: 2; found: 1 linear symmetries. Trying reduction of order `, `2nd order, trying reduction of order with given symmetries:`[x, y]
Solving time : 0.089
(sec)
Leaf size : 106
dsolve(y(x)^2*diff(diff(y(x),x),x) = x, y(x),singsol=all)