Internal problem ID [5640]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+3 x y^{\prime }+y-\frac {2}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=2/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \relax (x ) c_{1}}{x}+\frac {\ln \relax (x )^{2}}{x}+\frac {c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 20
DSolve[x^2*y''[x]+3*x*y'[x]+y[x]==2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (x) (\log (x)+c_2)+c_1}{x} \\ \end{align*}