67.2.19 problem Problem 2(d)

Internal problem ID [13905]
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(d)
Date solved : Monday, March 31, 2025 at 08:17:42 AM
CAS classification : [[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

\begin{align*} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \end{align*}

✗ Maple

ode:=sin(diff(diff(y(x),x),x))+y(x)*diff(diff(diff(diff(y(x),x),x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=Sin[D[y[x],{x,2}]]+y[x]*D[y[x],{x,4}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), (x, 4)) + sin(Derivative(y(x), (x, 2))) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve y(x)*Derivative(y(x), (x, 4)) + sin(Derivative(y(x), (x, 2))) - 1