10.8.22 problem 36

Internal problem ID [1294]
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 : 36
Date solved : Monday, January 27, 2025 at 04:50:11 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(t^2*diff(y(t),t$2)+ 4*t*diff(y(t),t)+2*y(t) = 0,y(t), singsol=all)
 

\[ y = \frac {c_2 t +c_1}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 34

DSolve[t^2*D[y[t],{t,2}]+4*t*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^{-\frac {3}{2}-\frac {\sqrt {5}}{2}} \left (c_2 t^{\sqrt {5}}+c_1\right ) \]