73.17.50 problem 50

Internal problem ID [15584]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 08:02:48 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=1/x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==1/x,y[x],x,IncludeSingularSolutions -> True]
 

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