22.14 problem 719

Internal problem ID [15463]

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.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

✓ 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]
                                                                                    
                                                                                    
 

\[ y(x)\to e^{-x} (x-1) \]