problem 1838

Internal problem ID [10160]
Internal ﬁle name [OUTPUT/9107_Monday_June_06_2022_06_39_52_AM_52633628/index.tex]
Book: Diﬀerential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1838.
ODE order: 3.
ODE degree: 1.
Maple trace
`Methods for third order ODEs: 
--- Trying classification methods --- 
trying 3rd order ODE linearizable_by_differentiation 
differential order: 3; trying a linearization to 4th order 
trying differential order: 3; missing variables 
`, `-> Computing symmetries using: way = 3 
`, `-> Computing symmetries using: way = exp_sym 
-> Calling odsolve with the ODE`, (diff(diff(_b(_a), _a), _a))*_b(_a)^2+(diff(_b(_a), _a))^2*_b(_a)+(diff(_b(_a), _a))*_b(_a)*_a-_b( 
   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) 
      --- 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) 
   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) 
   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 
   -> trying 2nd order, the S-function method 
      -> trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for the S-function 
      -> trying 2nd order, the S-function method 
      -> trying 2nd order, No Point Symmetries Class V 
         --- trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for dynamical symmetries --- 
         -> trying 2nd order, No Point Symmetries Class V 
      -> trying 2nd order, No Point Symmetries Class V 
         --- trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for dynamical symmetries --- 
         -> trying 2nd order, No Point Symmetries Class V 
      -> trying 2nd order, No Point Symmetries Class V 
         --- trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for dynamical symmetries --- 
         -> trying 2nd order, No Point Symmetries Class V 
   trying 2nd order, integrating factor of the form mu(x,y)/(y)^n, only the general case 
   -> trying 2nd order, dynamical_symmetries, only a reduction of order through one integrating factor of the form G(x,y)/(1+H(x,y)* 
      --- trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for dynamical symmetries --- 
      -> trying 2nd order, dynamical_symmetries, only a reduction of order through one integrating factor of the form G(x,y)/(1+H(x, 
   --- Trying Lie symmetry methods, 2nd order --- 
   `, `-> Computing symmetries using: way = 3 
   `, `-> Computing symmetries using: way = 5 
   `, `-> Computing symmetries using: way = formal 
trying differential order: 3; exact nonlinear 
Trying the formal computation of integrating factors depending on any 2 of [x, y, y, y] 
--- Trying Lie symmetry methods, high order --- 
`, `-> Computing symmetries using: way = 3 
`, `-> Computing symmetries using: way = 5 
`, `-> Computing symmetries using: way = formal 
            *** Sublevel 2 *** 
            Methods for first order ODEs: 
            --- Trying classification methods --- 
            trying a quadrature 
            trying 1st order linear 
            <- 1st order linear successful 
   -> Calling odsolve with the ODE`, diff(y(x), x), y(x)`      *** Sublevel 2 *** 
      Methods for first order ODEs: 
      --- Trying classification methods --- 
      trying a quadrature 
      trying 1st order linear 
      <- 1st order linear successful`
8.2 problem 1838
