15.5.8 problem 8

Internal problem ID [2944]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 8
Date solved : Sunday, March 30, 2025 at 01:00:32 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 5.85 (sec). Leaf size: 35

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

\begin{align*} y(x)\to -\frac {1}{x W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.815 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = x e^{C_{1} + W\left (- \frac {e^{- C_{1}}}{x^{2}}\right )} \]