Internal problem ID [15463]
Internal file name [OUTPUT/15464_Wednesday_May_08_2024_04_00_53_PM_73637771/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: 720.
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_high_order, _missing_x]]
Unable to solve or complete the solution.
Maple trace
`Methods for high 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: 5
dsolve([diff(y(x),x$4)-lambda^4*y(x)=0,y(0) = 0, (D@@2)(y)(0) = 0, y(Pi) = 0, (D@@2)(y)(Pi) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 6
DSolve[{y''''[x]-\[Lambda]^4*y[x]==0,{y[0]==0,y''[0]==0,y[Pi]==0,y''[Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 0 \]