73.8.12 problem 13.2 (f)

Internal problem ID [15141]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.2 (f)
Date solved : Thursday, March 13, 2025 at 05:47:38 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.130 (sec). Leaf size: 20

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

\begin{align*} y &= 0 \\ y &= \frac {{\mathrm e}^{\left (x +c_{2} \right ) c_{1}}+1}{c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 1.583 (sec). Leaf size: 26

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

\begin{align*} y(x)\to \frac {1+e^{c_1 (x+c_2)}}{c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(4*y(x)*Derivative(y(x), (x, 2)) + 1)/2 + Derivative(y(x), x) + 1/2 cannot be solved by the factorable group method