Internal problem ID [15462]
Internal file name [OUTPUT/15463_Wednesday_May_08_2024_04_00_53_PM_48923003/index.tex]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 17. Boundary value problems. Exercises page
163
Problem number: 719.
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_3rd_order, _missing_x]]
Unable to solve or complete the solution.
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying a quadrature checking if the LODE has constant coefficients <- constant coefficients successful`
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x$3)+diff(y(x),x$2)-diff(y(x),x)-y(x)=0,y(0) = -1, y(1) = 0, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 14
DSolve[{y'''[x]+y''[x]-y'[x]-y[x]==0,{y[0]==-1,y[1]==0,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} (x-1) \]