10.8.26 problem 40

Internal problem ID [1298]
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 : 40
Date solved : Monday, January 27, 2025 at 04:50:18 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 24

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

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