Internal problem ID [4164]
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 35.23(a), page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x y y^{\prime \prime }-2 x \left (y^{\prime }\right )^{2}+y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 18
dsolve(x*y(x)*diff(y(x),x$2)-2*x*(diff(y(x),x))^2+y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -\frac {1}{c_{1} \ln \relax (x )+c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 17
DSolve[x*y[x]*y''[x]-2*x*(y'[x])^2+y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2}{-\log (x)+c_1} \\ \end{align*}