80.9.4 problem 8

Internal problem ID [18595]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 63. Problems at page 196
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:03:26 PM
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)
 

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

✓ Solution by Mathematica

Time used: 0.020 (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]
 

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