10.9.25 problem 40

Internal problem ID [1327]
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 : 40
Date solved : Monday, January 27, 2025 at 04:51:04 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(t^2*diff(y(t),t$2)-3*t*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

DSolve[t^2*D[y[t],{t,2}]-3*t*D[y[t],t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 (2 c_2 \log (t)+c_1) \]