23.2.116 problem 118

Internal problem ID [5471]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 118
Date solved : Tuesday, September 30, 2025 at 12:44:11 PM
CAS classification : [[_homogeneous, `class G`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 796

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.098 (sec). Leaf size: 1553

ode=x (D[y[x],x])^2-2 y[x] D[y[x],x]+a==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out