Internal problem ID [4663]
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 35.13, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-3 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 33
dsolve(y(x)*diff(y(x),x$2)-3*(diff(y(x),x))^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {1}{\sqrt {-2 c_{1} x -2 c_{2}}} y \left (x \right ) = -\frac {1}{\sqrt {-2 c_{1} x -2 c_{2}}} \end{align*}
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 14
DSolve[y[x]*y''[x]-(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^{c_1 x} \]