10.9.17 problem 23

Internal problem ID [1319]
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 : 23
Date solved : Monday, January 27, 2025 at 04:50:58 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

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

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