83.23.30 problem 30

Internal problem ID [19240]
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 : 30
Date solved : Monday, March 31, 2025 at 07:01:50 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out