76.46.3 problem Ex. 3

Internal problem ID [20259]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 101
Problem number : Ex. 3
Date solved : Thursday, October 02, 2025 at 05:38:02 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

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

\[ y = c_2 \ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to c_1 \log (x)+c_2 \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 8

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

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