81.1.11 problem 10

Internal problem ID [18606]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 12:03:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y&=\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+5*y(x)=1/x,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x +\frac {1}{12 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+5*y[x]==1/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^5+\frac {1}{12 x}+c_1 x \]