73.17.50 problem 50

Internal problem ID [15513]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 50
Date solved : Monday, March 31, 2025 at 01:40:04 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+y(x) = 1/x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 27

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==1/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\log ^2(x)+2 c_2 \log (x)+2 c_1}{2 x} \]

✓ Sympy. Time used: 0.300 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) + y(x) - 1/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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