81.13.6 problem 17-6

Internal problem ID [21680]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 17. Reduction of Order. Page 420
Problem number : 17-6
Date solved : Thursday, October 02, 2025 at 07:59:52 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+1/x*diff(y(x),x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2}+c_1 \ln \left (x \right )+c_2 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

ode=D[y[x],{x,2}]+1/x*D[y[x],x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2}{2}+c_1 \log (x)+c_2 \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 14

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

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