83.23.26 problem 26

Internal problem ID [19236]
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 : 26
Date solved : Monday, March 31, 2025 at 07:00:28 PM
CAS classification : [_rational]

\begin{align*} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+x y&=0 \end{align*}

✓ Maple. Time used: 0.324 (sec). Leaf size: 866

ode:=x*y(x)*diff(y(x),x)^2-(x^2+y(x)^2-1)*diff(y(x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.276 (sec). Leaf size: 54

ode=x*y[x]*D[y[x],x]^2-(x^2+y[x]^2-1)*D[y[x],x]+x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)*Derivative(y(x), x)**2 + x*y(x) - (x**2 + y(x)**2 - 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out