10.9.29 problem 44

Internal problem ID [1331]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 44
Date solved : Monday, January 27, 2025 at 04:51:10 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(4*t^2*diff(y(t),t$2)-8*t*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_2 \ln \left (t \right )+c_1 \right ) t^{{3}/{2}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 25

DSolve[4*t^2*D[y[t],{t,2}]-8*t*D[y[t],t]+9*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} t^{3/2} (3 c_2 \log (t)+2 c_1) \]