80.1.6 problem 16 (a)

Internal problem ID [18465]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 16 (a)
Date solved : Monday, March 31, 2025 at 05:30:07 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \end{align*}

✗ Maple

ode:=diff(diff(v(u),u),u) = (1/v(u)+diff(v(u),u)^4)^(1/3); 
dsolve(ode,v(u), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[v[u],{u,2}]==(1/v[u]+D[v[u],u]^4)^(1/3); 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
u = symbols("u") 
v = Function("v") 
ode = Eq(-(Derivative(v(u), u)**4 + 1/v(u))**(1/3) + Derivative(v(u), (u, 2)),0) 
ics = {} 
dsolve(ode,func=v(u),ics=ics)
 

NotImplementedError : The given ODE -(Derivative(v(u), (u, 2))**3 - 1/v(u))**(1/4) + Derivative(v(u), u) cannot be solved by the factorable group method