14.10.3 problem Problem 16

Internal problem ID [3775]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with Nonconstant Coefficients. page 567
Problem number : Problem 16
Date solved : Tuesday, September 30, 2025 at 06:57:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+9 y&=9 \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+9*y(x) = 9*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (3 \ln \left (x \right )\right ) c_2 +\cos \left (3 \ln \left (x \right )\right ) c_1 +\ln \left (x \right ) \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 24

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]+9*y[x]==9*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (x)+c_1 \cos (3 \log (x))+c_2 \sin (3 \log (x)) \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) + 9*y(x) - 9*log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (3 \log {\left (x \right )} \right )} + C_{2} \cos {\left (3 \log {\left (x \right )} \right )} + \log {\left (x \right )} \]