32.10.13 problem Exercise 35.13, page 504

Internal problem ID [6007]
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 35.13, page 504
Date solved : Monday, January 27, 2025 at 01:32:06 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 33

dsolve(y(x)*diff(y(x),x$2)-3*(diff(y(x),x))^2=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \frac {1}{\sqrt {-2 c_1 x -2 c_2}} \\ y &= -\frac {1}{\sqrt {-2 c_1 x -2 c_2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 14

DSolve[y[x]*D[y[x],{x,2}]-(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 e^{c_1 x} \]