76.12.9 problem 15

Internal problem ID [17565]
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 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 10:44:08 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 18

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

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