56.1.49 problem 49

Internal problem ID [8761]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 49
Date solved : Monday, January 27, 2025 at 04:48:26 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(t^2*diff(y(t),t$2)-3*t*diff(y(t),t)+5*y(t)=0,y(t), singsol=all)
 

\[ y = t^{2} \left (c_{1} \sin \left (\ln \left (t \right )\right )+c_{2} \cos \left (\ln \left (t \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 22

DSolve[t^2*D[y[t],{t,2}]-3*t*D[y[t],t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 (c_2 \cos (\log (t))+c_1 \sin (\log (t))) \]