Internal problem ID [4154]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }+\left (y^{\prime }\right )^{3}-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 44
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 \relax (x ) = 0 \\ y \relax (x ) = c_{1} \\ y \relax (x ) = {\mathrm e}^{-\frac {c_{1} \LambertW \left (\frac {{\mathrm e}^{\frac {c_{2}}{c_{1}}} {\mathrm e}^{\frac {x}{c_{1}}}}{c_{1}}\right )-c_{2}-x}{c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 29
DSolve[y[x]*y''[x]+(y'[x])^3-(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{c_1} \text {ProductLog}\left (e^{e^{-c_1} (x+c_2)-c_1}\right ) \\ \end{align*}