18.14 problem 27.4

Internal problem ID [13862]

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: 4.516 (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]
                                                                                    
                                                                                    
 

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