15.18.31 problem 31

Internal problem ID [3274]
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 : 31
Date solved : Sunday, March 30, 2025 at 01:26:08 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=\frac {\sqrt {2}}{2} \end{align*}

✓ Maple. Time used: 0.101 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x) = y(x)^3; 
ic:=y(0) = -1, D(y)(0) = 1/2*2^(1/2); 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\sqrt {2}}{x +\sqrt {2}} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 18

ode=D[y[x],{x,2}]==y[x]^3; 
ic={y[0]==1,Derivative[1][y][0] ==Sqrt[2]/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {2}{\sqrt {2} x-2} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**3 + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(x), x), x, 0): sqrt(2)/2} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out