13.13.8 problem 7

Internal problem ID [2438]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8.1, Singular points, Euler equations. Page 201
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:52:50 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

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

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

\[ y = c_1 \sin \left (\ln \left (t \right )\right )+c_2 \cos \left (\ln \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 18

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

\[ y(t)\to c_1 \cos (\log (t))+c_2 \sin (\log (t)) \]