20.10.3 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 : Monday, January 27, 2025 at 08:01:21 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*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 24

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

\[ y(x)\to \log (x)+c_1 \cos (3 \log (x))+c_2 \sin (3 \log (x)) \]