84.2.4 problem 1.9

Internal problem ID [22073]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts. Supplementary problems
Problem number : 1.9
Date solved : Thursday, October 02, 2025 at 08:23:26 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+\sin \left (y\right )&=0 \end{align*}

✗ Maple

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+x*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+sin(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,4}]+x*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-x*D[y[x],x]+Sin[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + x*Derivative(y(x), (x, 3)) + sin(y(x)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(x*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3))) + sin(y(x)) + Derivative(y(x), (x, 4)))/x cannot be solved by the factorable group method