66.2.43 problem Problem 58

Internal problem ID [13942]
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 : Tuesday, January 28, 2025 at 06:09:17 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*}

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 11

dsolve([diff(y(x),x$2)=2*y(x)^3,y(1) = 1, D(y)(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 12

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

\[ y(x)\to \frac {1}{2-x} \]