60.7.133 problem 1748 (book 6.157)

Internal problem ID [11683]
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 : Wednesday, March 05, 2025 at 02:40:15 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*}

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

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

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

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

ode=-5*D[y[x],x]^2 + 3*y[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x)*Derivative(y(x), (x, 2)) - 5*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(15)*sqrt(y(x)*Derivative(y(x), (x, 2)))/5 + Derivative(y(x), x) cannot be solved by the factorable group method