14.13.10 problem 10

Internal problem ID [2637]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8.1, singular points, Euler equations. Excercises page 203
Problem number : 10
Date solved : Monday, January 27, 2025 at 06:05:06 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*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve([t^2*diff(y(t),t$2)-3*t*diff(y(t),t)+4*y(t)=0,y(1) = 1, D(y)(1) = 0],y(t), singsol=all)
 

\[ y = t^{2} \left (1-2 \ln \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 15

DSolve[{t^2*D[y[t],{t,2}]-3*t*D[y[t],t]+4*y[t]==0,{y[1]==1,Derivative[1][y][1] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 (1-2 \log (t)) \]