28.1.45 problem 46

Internal problem ID [4351]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 46
Date solved : Sunday, March 30, 2025 at 03:09:15 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 19

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

\[ y = -\frac {\operatorname {LambertW}\left (-x^{3} {\mathrm e}^{-3 c_1}\right )}{x^{2}} \]

✓ Mathematica. Time used: 2.24 (sec). Leaf size: 33

ode=(2*x^2*y[x]^2+y[x])+(x^3*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^3\right )}{x^2} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.590 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \frac {W\left (C_{1} x^{3}\right )}{x^{2}} \]