10.8.24 problem 38

Internal problem ID [1296]
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 : 38
Date solved : Monday, January 27, 2025 at 04:50:15 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(t^2*diff(y(t),t$2)- 4*t*diff(y(t),t)-6*y(t) = 0,y(t), singsol=all)
 

\[ y = \frac {c_1 \,t^{7}+c_2}{t} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[t^2*D[y[t],{t,2}]-4*t*D[y[t],t]-6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_2 t^7+c_1}{t} \]