Internal problem ID [5433]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 26.
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]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^3=0,y(x), singsol=all)
\begin{align*} y = 0 y = c_{1} y = {\mathrm e}^{\operatorname {LambertW}\left (\left (x +c_{2} \right ) {\mathrm e}^{c_{1}} {\mathrm e}^{-1}\right )-c_{1} +1} \end{align*}
✓ Solution by Mathematica
Time used: 60.092 (sec). Leaf size: 26
DSolve[y[x]*y''[x]+y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x+c_2}{W\left (e^{-1-c_1} (x+c_2)\right )} \]