50.14.23 problem 3(g)

Internal problem ID [8061]
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)
Date solved : Monday, January 27, 2025 at 03:41:07 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {2}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=2/x,y(x), singsol=all)
 

\[ y = \frac {c_{2} +\ln \left (x \right )^{2}+c_{1} \ln \left (x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==2/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\log ^2(x)+c_2 \log (x)+c_1}{x} \]