Internal problem ID [4155]
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]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }-3 \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (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 \relax (x ) = 0 \\ y \relax (x ) = \frac {1}{\sqrt {-2 c_{1} x -2 c_{2}}} \\ y \relax (x ) = -\frac {1}{\sqrt {-2 c_{1} x -2 c_{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 14
DSolve[y[x]*y''[x]-(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 e^{c_1 x} \\ \end{align*}