Internal problem ID [4152]
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 35.10, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }+\left (y^{\prime }\right )^{2}-y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.082 (sec). Leaf size: 37
dsolve(y(x)*diff(y(x),x$2)+(diff(y(x),x))^2-diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -c_{1} \left (\LambertW \left (-\frac {{\mathrm e}^{-1} {\mathrm e}^{-\frac {c_{2}}{c_{1}}} {\mathrm e}^{-\frac {x}{c_{1}}}}{c_{1}}\right )+1\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 32
DSolve[y[x]*y''[x]+(y'[x])^2-y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -c_1 \left (1+\text {ProductLog}\left (-\frac {e^{-\frac {x+c_1+c_2}{c_1}}}{c_1}\right )\right ) \\ \end{align*}