33.4.6 problem Problem 12.14

Internal problem ID [7827]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.14
Date solved : Tuesday, September 30, 2025 at 05:06:02 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = c_1 x +\frac {c_2}{x}+\frac {x^{2} \left (3 \ln \left (x \right )-4\right )}{9} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to -\frac {4 x^2}{9}+\frac {1}{3} x^2 \log (x)+c_2 x+\frac {c_1}{x} \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{2} \left (C_{2} + 3 x \log {\left (x \right )} - 4 x\right )}{9}}{x} \]