Internal problem ID [1481]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient.
Page 483
Problem number: section 9.2, problem 17.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 9, y^{\prime \prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve([diff(y(x),x$3)-diff(y(x),x$2)-diff(y(x),x)+y(x)=0,y(0) = -2, D(y)(0) = 9, (D@@2)(y)(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = -4 \,{\mathrm e}^{-x}+\left (3 x +2\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[{y'''[x]-y''[x]-y'[x]+y[x]==0,{y[0]==-2,y'[0]==9,y''[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (3 x+2)-4 e^{-x} \\ \end{align*}