75.22.14 problem 719

Internal problem ID [17193]
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 ODEs). Section 17. Boundary value problems. Exercises page 163
Problem number : 719
Date solved : Tuesday, January 28, 2025 at 09:56:52 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y \left (1\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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)
 

\[ y = {\mathrm e}^{-x} \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 14

DSolve[{D[y[x],{x,3}]+D[y[x],{x,2}]-D[y[x],x]-y[x]==0,{y[0]==-1,y[1]==0,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

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