Internal problem ID [11850]
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 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+2/(1-y(x))*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x +c_{2} -1}{c_{1} x +c_{2}} \]
✓ Solution by Mathematica
Time used: 0.298 (sec). Leaf size: 37
DSolve[y''[x]+2/(1-y[x])*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x-1+c_2 c_1}{c_1 (x+c_2)} y(x)\to 1 y(x)\to \text {Indeterminate} \end{align*}