76.13.49 problem 58

Internal problem ID [17631]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 58
Date solved : Tuesday, January 28, 2025 at 10:46:08 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

\[ y = \frac {c_{2} x^{3}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 18

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

\[ y(x)\to \frac {c_2 x^3+c_1}{x} \]