Internal problem ID [5058]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number: 50.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(x),x$2)+1/x*diff(y(x),x)-1/x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[y''[x]+1/x*y'[x]-1/x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x}+c_2 x \\ \end{align*}