Internal problem ID [2095]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[x^2*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x}+c_2 x \\ \end{align*}