60.7.157 problem 1748 (book 6.157)

Internal problem ID [11746]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1748 (book 6.157)
Date solved : Monday, January 27, 2025 at 11:33:31 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} 3 y^{\prime \prime } y-5 {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 21

dsolve(3*diff(diff(y(x),x),x)*y(x)-5*diff(y(x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ -\frac {3}{2 y^{{2}/{3}}}-c_{1} x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.181 (sec). Leaf size: 25

DSolve[-5*D[y[x],x]^2 + 3*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_2}{(2 x+3 c_1){}^{3/2}} \\ y(x)\to 0 \\ \end{align*}