84.8.3 problem 4.12

Internal problem ID [22115]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.12
Date solved : Thursday, October 02, 2025 at 08:25:23 PM
CAS classification : [_quadrature]

\begin{align*} \frac {1}{x}+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 10

ode:=1/x+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=1/x+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 7

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

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