Internal problem ID [10162]
Internal file name [OUTPUT/9109_Monday_June_06_2022_06_40_19_AM_53447690/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1840.
ODE order: 3.
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)+(diff(_b(_a), _a))*_b(_a)*_a*a = symmetry methods on request `, `2nd order, trying reduction of order with given symmetries:`[_a, 2*_b]
✗ Solution by Maple
dsolve(diff(diff(diff(y(x),x),x),x)+a*y(x)*diff(diff(y(x),x),x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[a*y[x]*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved