73.8.10 problem 13.2 (d)

Internal problem ID [15147]
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 (d)
Date solved : Monday, March 31, 2025 at 01:29:17 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 17

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

\[ y = -\frac {\ln \left (c_1 x -1\right )}{c_1}+c_2 \]

✓ Mathematica. Time used: 1.073 (sec). Leaf size: 42

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

\[ y(x)\to \int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ][c_1+\log (K[2])]dK[2]+c_2 \]

✓ Sympy. Time used: 0.835 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} - \frac {\log {\left (C_{2} x - 1 \right )}}{C_{2}} \]