10.8.28 problem 42

Internal problem ID [1300]
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 : 42
Date solved : Monday, January 27, 2025 at 04:50:23 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(t^2*diff(y(t),t$2)+ 7*t*diff(y(t),t)+10*y(t) = 0,y(t), singsol=all)
 

\[ y = \frac {c_1 \sin \left (\ln \left (t \right )\right )+c_2 \cos \left (\ln \left (t \right )\right )}{t^{3}} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 22

DSolve[t^2*D[y[t],{t,2}]+7*t*D[y[t],t]+10*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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