73.18.14 problem 27.4

Internal problem ID [15598]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.4
Date solved : Tuesday, January 28, 2025 at 08:03:00 AM
CAS classification : [_Lienard]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.483 (sec). Leaf size: 7

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

\[ y = \operatorname {BesselJ}\left (0, t\right ) \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 8

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

\[ y(t)\to \operatorname {BesselJ}(0,t) \]