10.8.27 problem 41

Internal problem ID [1299]
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 : 41
Date solved : Monday, January 27, 2025 at 04:50:21 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

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

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

\[ y = \frac {c_1 \,t^{4}+c_2}{t^{3}} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

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

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