60.2.43 problem Problem 58

Internal problem ID [15223]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 58
Date solved : Thursday, October 02, 2025 at 10:07:29 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }&=2 y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ y^{\prime }\left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.062 (sec). Leaf size: 11

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

\[ y = -\frac {1}{x -2} \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to \frac {1}{2-x} \end{align*}

✗ Sympy

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

Timed Out