15.8.4 problem 4

Internal problem ID [3007]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 4
Date solved : Tuesday, March 04, 2025 at 03:43:05 PM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 14

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

\[ y(x)\to \frac {x+c_1}{\log (x)} \]

✓ Sympy. Time used: 0.244 (sec). Leaf size: 8

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

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