8.7.27 problem 52

Internal problem ID [833]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 52
Date solved : Monday, January 27, 2025 at 03:09:27 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {c_2 \,x^{2}+c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

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

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