40.2.5 problem 28

Internal problem ID [6583]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 28
Date solved : Wednesday, March 05, 2025 at 12:58:33 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 7.828 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 0.563 (sec). Leaf size: 12

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)
 

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