82.6.1 problem Ex. 1

Internal problem ID [18663]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 22
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 12:31:38 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 15

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

\[ y(x)\to -\log (x)+c_1 x-1 \]

✓ Sympy. Time used: 0.224 (sec). Leaf size: 10

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

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