76.23.10 problem Ex. 11

Internal problem ID [20151]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 11
Date solved : Thursday, October 02, 2025 at 05:33:19 PM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.409 (sec). Leaf size: 76

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

\begin{align*} y(x)&\to \sqrt {c_1 \left (x^2+\frac {2}{-1+c_1}\right )}\\ y(x)&\to -x-\sqrt {2}\\ y(x)&\to \sqrt {2}-x\\ y(x)&\to x-\sqrt {2}\\ y(x)&\to x+\sqrt {2} \end{align*}

✗ Sympy

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

Timed Out