2.5 problem Problem 1(e)

Internal problem ID [12225]
Internal file name [OUTPUT/10878_Thursday_September_28_2023_01_05_45_AM_84918379/index.tex]

Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number: Problem 1(e).
ODE order: 2.
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, _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(y(x), x), x))+1)/y(x), y(x), _mu = F(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))*_b(_a)^3+(4*(diff(diff(_b(_a), _a), _a))*_b(_a)^2*(diff(_b( 
   symmetry methods on request 
`, `high order, trying reduction of order with given symmetries:`[_a, 1/2*_b]
 

✗ Solution by Maple

dsolve(diff(y(x),x$2)+y(x)*diff(y(x),x$4)=1,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y''[x]+y[x]*y''''[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

Not solved