Internal problem ID [13183]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.5 (g).
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]]
\[ \boxed {y y^{\prime \prime }-2 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(y(x)*diff(y(x),x$2)=2*diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = -\frac {1}{c_{1} x +c_{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 19
DSolve[y[x]*y''[x]==2*y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2}{x+c_1} y(x)\to 0 \end{align*}