Internal problem ID [2804]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+9 y=9 \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.155 (sec). Leaf size: 24
DSolve[x^2*y''[x]+x*y'[x]+9*y[x]==9*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log (x)+c_1 \cos (3 \log (x))+c_2 \sin (3 \log (x)) \]