62.18.1 problem Ex 1

Internal problem ID [12841]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 30. Page 63
Problem number : Ex 1
Date solved : Monday, March 31, 2025 at 07:21:22 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

\begin{align*} y&=y^{\prime } x +\frac {1}{y^{\prime }} \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 27

ode:=y(x) = x*diff(y(x),x)+1/diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -2 \sqrt {x} \\ y &= 2 \sqrt {x} \\ y &= c_1 x +\frac {1}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 41

ode=y[x]==D[y[x],x]*x+1/D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x+\frac {1}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {x} \\ y(x)\to 2 \sqrt {x} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x) - 1/Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out