32.6.15 problem Exercise 12.15, page 103

Internal problem ID [5880]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.15, page 103
Date solved : Sunday, March 30, 2025 at 10:22:38 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{2}} \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 22

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

\begin{align*} y(x)\to c_1 e^{-x/2} \log (x) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.285 (sec). Leaf size: 12

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

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