12.18.17 problem section 9.2, problem 17

Internal problem ID [2131]
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
Date solved : Monday, January 27, 2025 at 05:42:42 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 )&=-2\\ y^{\prime }\left (0\right )&=9\\ y^{\prime \prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

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)
 

\[ y = -4 \,{\mathrm e}^{-x}+\left (3 x +2\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

DSolve[{D[y[x],{x,3}]-D[y[x],{x,2}]-D[y[x],x]+y[x]==0,{y[0]==-2,Derivative[1][y][0] ==9,Derivative[2][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (3 x+2)-4 e^{-x} \]