Internal problem ID [13861]
Internal file name [OUTPUT/13033_Friday_February_23_2024_06_54_16_AM_99659885/index.tex]
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.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[_Lienard]
Unable to solve or complete the solution.
Unable to parse ODE.
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying a quadrature checking if the LODE has constant coefficients checking if the LODE is of Euler type trying a symmetry of the form [xi=0, eta=F(x)] checking if the LODE is missing y -> Trying a Liouvillian solution using Kovacics algorithm <- No Liouvillian solutions exists -> Trying a solution in terms of special functions: -> Bessel <- Bessel successful <- special function solution successful`
✓ 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]
\[ y(t)\to \operatorname {BesselJ}(0,t) \]