problem 1841

Internal problem ID [10163]
Internal ﬁle name [OUTPUT/9110_Monday_June_06_2022_06_40_33_AM_68056272/index.tex]
Book: Diﬀerential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1841.
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 
trying differential order: 3; exact nonlinear 
-> Calling odsolve with the ODE`, _a^2*(diff(diff(_b(_a), _a), _a))+_a*_b(_a)^2-(diff(_b(_a), _a))*_a-(Int(f(_a), _a))+c__1 = 0, _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 the formal computation of integrating factors depending on any 2 of [x, y, y, y] 
         *** 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))*x-2*y(x), y(x)`   *** Sublevel 2 *** 
   Methods for first order ODEs: 
   --- Trying classification methods --- 
   trying a quadrature 
   trying 1st order linear 
   <- 1st order linear successful 
Successful computation of 1 integrating factor: [x^2] 
Attempting computing related first integrals... 
differential order: 3; looking for linear symmetries 
--- Trying Lie symmetry methods, high order --- 
`, `-> Computing symmetries using: way = 3 
`, `-> Computing symmetries using: way = 5`
8.5 problem 1841
