Internal problem ID [13542]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (t \right ) = \operatorname {BesselJ}\left (0, t\right ) \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 8
DSolve[{t*y''[t]+y'[t]+t*y[t]==0,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \operatorname {BesselJ}(0,t) \]