85.20.1 problem 2

Internal problem ID [22562]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 52
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:51:32 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 25

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

\[ y = \frac {-x^{2}+\operatorname {LambertW}\left (-2 x \,{\mathrm e}^{x^{2}} c_1 \,{\mathrm e}^{-1}\right )}{x} \]

✓ Mathematica. Time used: 5.083 (sec). Leaf size: 33

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

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

✗ Sympy

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

Timed Out