12.4.4 problem 4

Internal problem ID [1611]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 4
Date solved : Thursday, March 13, 2025 at 04:01:26 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -(x**2 + y(x)**2)/log(x*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method