68.15.26 problem 26

Internal problem ID [17752]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 26
Date solved : Thursday, October 02, 2025 at 02:27:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-16*y(x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{4}}+c_1 \,x^{4}-\frac {\ln \left (x \right )}{16} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]-16*y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^4+\frac {c_1}{x^4}-\frac {\log (x)}{16} \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 16*y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{4}} + C_{2} x^{4} - \frac {\log {\left (x \right )}}{16} \]