54.1.190 problem 193

Internal problem ID [11504]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 193
Date solved : Tuesday, September 30, 2025 at 08:48:14 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to a x+\frac {c_1}{\log (x)} \end{align*}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 10

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

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