Internal problem ID [4673]
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(b), page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 35
dsolve(x*y(x)*diff(y(x),x$2)+x*(diff(y(x),x))^2-y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \sqrt {c_{1} x^{2}+2 c_{2}} y \left (x \right ) = -\sqrt {c_{1} x^{2}+2 c_{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.241 (sec). Leaf size: 18
DSolve[x*y[x]*y''[x]+x*(y'[x])^2-y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sqrt {x^2+c_1} \]