Internal problem ID [4356]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }-x y-\frac {1}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x)-x*y(x)=1/x,y(x), singsol=all)
\[ y \relax (x ) = \left (-\frac {1}{3 x^{3}}+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 17
DSolve[x^2*y'[x]-x*y[x]==1/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3 x^2}+c_1 x \\ \end{align*}