9.10 problem 14.1 (j)

Internal problem ID [13534]
Internal file name [OUTPUT/12706_Friday_February_16_2024_12_11_09_AM_4665780/index.tex]

Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number: 14.1 (j).
ODE order: 2.
ODE degree: 1.

The type(s) of ODE detected by this program : "unknown"

Maple gives the following as the ode type

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

Unable to solve or complete the solution.

Unable to parse ODE.

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)*_a+6*(diff(_b(_a), _a))*_b(_a)+ 
   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`
 

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x$3)+6*diff(y(x),x$2)+3*diff(y(x),x)=y(x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y[x]*y'''[x]+6*y''[x]+3*y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved