35.8.1 problem 1

Internal problem ID [6208]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 1
Date solved : Monday, January 27, 2025 at 01:47:43 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

\[ y = \left (-\frac {1}{3 x^{3}}+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 17

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

\[ y(x)\to -\frac {1}{3 x^2}+c_1 x \]