Internal problem ID [10172]
Internal file name [OUTPUT/9119_Monday_June_06_2022_06_41_53_AM_90921255/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1850.
ODE order: 4.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]
Unable to solve or complete the solution.
Unable to parse ODE.
Maple trace
`Methods for high order ODEs: --- Trying classification methods --- trying 4th order ODE linearizable_by_differentiation trying high order reducible trying differential order: 4; mu polynomial in y -> Calling odsolve with the ODE`, diff(diff(diff(diff(y(x), x), x), x), x) = ((diff(diff(diff(y(x), x), x), x))*(diff(diff(y(x), x), Integrating factor hint being investigated... trying differential order: 4; exact nonlinear trying differential order: 4; missing variables `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = exp_sym -> Calling odsolve with the ODE`, diff(diff(diff(_b(_a), _a), _a), _a) = (diff(diff(_b(_a), _a), _a))*(-_b(_a)^3+diff(_b(_a), _a))/_ symmetry methods on request `, `high order, trying reduction of order with given symmetries:`[1, 0], [_a, -1/2*_b]
✗ Solution by Maple
dsolve(diff(y(x),x)*diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^3*diff(diff(diff(y(x),x),x),x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]^3*Derivative[3][y][x] - y''[x]*Derivative[3][y][x] + y'[x]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved