10.5.11 problem 11

Internal problem ID [1203]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 11
Date solved : Thursday, March 13, 2025 at 03:55:19 PM
CAS classification : [[_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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