13.8.11 problem 19

Internal problem ID [2386]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.1, Complex roots. Page 141
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:51:13 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

\[ y = \frac {c_1 \sin \left (\frac {\sqrt {7}\, \ln \left (t \right )}{2}\right )+c_2 \cos \left (\frac {\sqrt {7}\, \ln \left (t \right )}{2}\right )}{\sqrt {t}} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 42

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

\[ y(t)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {7} \log (t)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {7} \log (t)\right )}{\sqrt {t}} \]