12.8.11 problem 14

Internal problem ID [1747]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 14
Date solved : Monday, January 27, 2025 at 05:34:12 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

\[ y = x \left (c_2 \ln \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 15

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

\[ y(x)\to x (c_2 \log (x)+c_1) \]