44.1.2 problem 2

Internal problem ID [6877]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 2
Date solved : Sunday, March 30, 2025 at 11:25:09 AM
CAS classification : [NONE]

\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \end{align*}

✗ Maple

ode:=x*diff(diff(diff(y(x),x),x),x)-diff(y(x),x)^4+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*D[y[x],{x,3}]-D[y[x],x]^4+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*Derivative(y(x), (x, 3)) + y(x) - Derivative(y(x), x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(x*Derivative(y(x), (x, 3)) + y(x))**(1/4) + Derivative(y(x), x) cannot be solved by the factorable group method