83.46.9 problem Ex 9 page 73

Internal problem ID [19503]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 9 page 73
Date solved : Monday, March 31, 2025 at 07:26:30 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} x^{2} {y^{\prime }}^{3}+y y^{\prime } \left (2 x +y\right )+y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.206 (sec). Leaf size: 1214

ode:=x^2*diff(y(x),x)^3+y(x)*diff(y(x),x)*(y(x)+2*x)+y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✗ Mathematica

ode=x^2*D[y[x],x]^3+y[x]*D[y[x],x]*(2*x+y[x])+y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**3 + (2*x + y(x))*y(x)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out