60.7.125 problem 1716 (book 6.125)

Internal problem ID [11714]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1716 (book 6.125)
Date solved : Monday, January 27, 2025 at 11:30:59 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime } y-a {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.076 (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 &= 0 \\ y &= \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: 0.400 (sec). Leaf size: 26

DSolve[-(a*D[y[x],x]^2) + y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 (-a x+x-c_1){}^{\frac {1}{1-a}} \]