14.7.11 problem 11

Internal problem ID [2555]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 11
Date solved : Monday, January 27, 2025 at 06:00:16 AM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 27

dsolve([t^2*diff(y(t),t$2)+5*t*diff(y(t),t)-2*y(t)=0,y(1) = 0, D(y)(1) = 1],y(t), singsol=all)
 

\[ y = \frac {\sqrt {6}\, \left (t^{\sqrt {6}}-t^{-\sqrt {6}}\right )}{12 t^{2}} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 36

DSolve[{t^2*D[y[t],{t,2}]+5*t*D[y[t],t]-2*y[t]==0,{y[1]==0,Derivative[1][y][1] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^{-2-\sqrt {6}} \left (t^{2 \sqrt {6}}-1\right )}{2 \sqrt {6}} \]