10.8.23 problem 37

Internal problem ID [1295]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 37
Date solved : Monday, January 27, 2025 at 04:50:13 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(t^2*diff(y(t),t$2)+ 3*t*diff(y(t),t)+125/100*y(t) = 0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 30

DSolve[t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+125/100*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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