60.1.107 problem 109

Internal problem ID [10121]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 109
Date solved : Sunday, March 30, 2025 at 03:17:07 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {1}{2+c_1 x +2 \ln \left (x \right )} \]

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {1}{2 \log (x)+c_1 x+2} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.233 (sec). Leaf size: 14

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

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