23.4.195 problem 195

Internal problem ID [6497]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 195
Date solved : Tuesday, September 30, 2025 at 03:02:20 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 21

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

\begin{align*} y &= 0 \\ \frac {5 y^{{4}/{5}}}{4}-c_1 x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 20

ode=5*y[x]*D[y[x],{x,2}] == D[y[x],x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 (4 x-5 c_1){}^{5/4} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(5)*sqrt(y(x)*Derivative(y(x), (x, 2))) + Derivative(y(x),