10.9.27 problem 42

Internal problem ID [1329]
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 : 42
Date solved : Monday, January 27, 2025 at 04:51:07 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

\[ y = c_1 t +c_2 \,t^{{5}/{2}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

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

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