32.10.6 problem Exercise 35.6, page 504

Internal problem ID [6000]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.6, page 504
Date solved : Monday, January 27, 2025 at 01:30:43 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \left (y+1\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 59

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

\begin{align*} y &= -1 \\ y &= -\frac {\sqrt {-2 c_1 x -2 c_2}-1}{\sqrt {-2 c_1 x -2 c_2}} \\ y &= -\frac {\sqrt {-2 c_1 x -2 c_2}+1}{\sqrt {-2 c_1 x -2 c_2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.461 (sec). Leaf size: 107

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

\begin{align*} y(x)\to -\frac {2 c_1 x+\sqrt {2} \sqrt {-c_1 (x+c_2)}+2 c_2 c_1}{2 c_1 (x+c_2)} \\ y(x)\to \frac {-2 c_1 x+\sqrt {2} \sqrt {-c_1 (x+c_2)}-2 c_2 c_1}{2 c_1 (x+c_2)} \\ y(x)\to -1 \\ y(x)\to \text {Indeterminate} \\ \end{align*}