Internal problem ID [10858]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }-2 y^{3}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = -\frac {1}{x -2} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 12
DSolve[{y''[x]==2*y[x]^3,{y[1]==1,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2-x} \\ \end{align*}