83.18.15 problem 15

Internal problem ID [19154]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 15
Date solved : Monday, March 31, 2025 at 06:49:54 PM
CAS classification : [_quadrature]

\begin{align*} x^{2} {y^{\prime }}^{3}+y \left (1+x^{2} y\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.096 (sec). Leaf size: 5

ode:=x^2*diff(y(x),x)^3+y(x)*(1+x^2*y(x))*diff(y(x),x)^2+y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \]

✗ Mathematica

ode=x^2*D[y[x],x]^3+y[x]*(1+x^2*y[x])*D[y[x],x]^2+y[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**3 + (x**2*y(x) + 1)*y(x)*Derivative(y(x), x)**2 + y(x)**2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out