47.2.53 problem 49

Internal problem ID [7469]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 49
Date solved : Wednesday, March 05, 2025 at 04:39:15 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 60.326 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{x^2 W\left (\frac {e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}}{x^2}\right )} \]

✓ Sympy. Time used: 0.771 (sec). Leaf size: 15

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

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