Internal problem ID [4662]
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]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= {\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: 22.229 (sec). Leaf size: 32
DSolve[y[x]*y''[x]+(y'[x])^3-(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{c_1} W\left (e^{e^{-c_1} \left (x-e^{c_1} c_1+c_2\right )}\right ) \]