Internal problem ID [10038]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1716 (book 6.125).
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]]
\[ \boxed {y^{\prime \prime } y-a {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 28
dsolve(diff(diff(y(x),x),x)*y(x)-a*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \left (-\frac {1}{\left (a -1\right ) \left (c_{1} x +c_{2} \right )}\right )^{\frac {1}{a -1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.736 (sec). Leaf size: 26
DSolve[-(a*y'[x]^2) + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 (-a x+x-c_1){}^{\frac {1}{1-a}} \]