15.18.4 problem 4

Internal problem ID [3247]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 4
Date solved : Sunday, March 30, 2025 at 01:23:50 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{3} y^{\prime \prime }+4&=0 \end{align*}

✓ Maple. Time used: 0.225 (sec). Leaf size: 52

ode:=y(x)^3*diff(diff(y(x),x),x)+4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {\left (-2+c_1 \left (c_2 +x \right )\right ) \left (2+c_1 \left (c_2 +x \right )\right ) c_1}}{c_1} \\ y &= -\frac {\sqrt {\left (-2+c_1 \left (c_2 +x \right )\right ) \left (2+c_1 \left (c_2 +x \right )\right ) c_1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 3.061 (sec). Leaf size: 93

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

\begin{align*} y(x)\to -\frac {\sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-4+c_2{}^2 c_1{}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-4+c_2{}^2 c_1{}^2}}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ \end{align*}

✗ Sympy

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

Timed Out