32.10.12 problem Exercise 35.12, page 504

Internal problem ID [6006]
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 35.12, page 504
Date solved : Monday, January 27, 2025 at 01:32:05 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 36

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

\begin{align*} y &= 0 \\ y &= c_1 \\ y &= {\mathrm e}^{\frac {-c_1 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {c_2 +x}{c_1}}}{c_1}\right )+c_2 +x}{c_1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 21.123 (sec). Leaf size: 32

DSolve[y[x]*D[y[x],{x,2}]+(D[y[x],x])^3-(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{c_1} W\left (e^{e^{-c_1} \left (x-e^{c_1} c_1+c_2\right )}\right ) \]