58.1.48 problem 48

Internal problem ID [9119]
Book : Second order enumerated odes
Section : section 1
Problem number : 48
Date solved : Sunday, March 30, 2025 at 02:07:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \end{align*}

✓ Maple. Time used: 1.725 (sec). Leaf size: 2829

ode:=y(x)*diff(diff(y(x),x),x)^4+diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 3.846 (sec). Leaf size: 1237

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

Too large to display

✗ Sympy

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

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