83.23.33 problem 32

Internal problem ID [19235]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 32
Date solved : Thursday, March 13, 2025 at 02:01:55 PM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.317 (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