2.22 problem Problem 2(h)

Internal problem ID [12242]
Internal file name [OUTPUT/10895_Thursday_September_28_2023_01_08_21_AM_1427532/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 2(h).
ODE order: 2.
ODE degree: 1.

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

Maple gives the following as the ode type

[NONE]

Unable to solve or complete the solution.

Unable to parse ODE.

Maple trace

`Methods for third order ODEs: 
Successful isolation of d^3y/dx^3: 2 solutions were found. Trying to solve each resulting ODE. 
   *** Sublevel 2 *** 
   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; exact nonlinear 
   trying 3rd order, integrating factor of the form mu(y) for some mu 
   Trying the formal computation of integrating factors depending on any 2 of [x, y, y, y] 
   differential order: 3; looking for linear symmetries`
 

✗ Solution by Maple

dsolve(diff(y(x),x$3)^2+sqrt(y(x))=sin(x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y'''[x]^2+Sqrt[y[x]]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved