47.4.2 problem 50

Internal problem ID [7479]
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
Date solved : Monday, January 27, 2025 at 03:01:48 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)+1/x*diff(y(x),x)-1/x^2*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{2}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 16

DSolve[D[y[x],{x,2}]+1/x*D[y[x],x]-1/x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x}+c_2 x \]