23.4.306 problem 309

Internal problem ID [6608]
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 : 309
Date solved : Tuesday, September 30, 2025 at 03:50:11 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime }&={y^{\prime }}^{2}-y y^{\prime \prime } \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 10

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

\[ y = {\mathrm e}^{c_{1} \left (c_2 +x \right )} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : multiple generators [_X0, f(_Dummy_37/_X0)] 
No algorithms are implemented to s