47.3.2 problem 2

Internal problem ID [7475]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.3. Exact equations problems. page 24
Problem number : 2
Date solved : Sunday, March 30, 2025 at 12:09:55 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y \ln \left (x \right )+\frac {y^{4}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.211 (sec). Leaf size: 1025

ode=y[x]/x+(y[x]^3+Log[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 72.611 (sec). Leaf size: 740

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

\[ \text {Solution too large to show} \]