12.18.24 problem section 9.2, problem 24

Internal problem ID [2138]
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 24
Date solved : Monday, January 27, 2025 at 05:42:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=-8\\ y^{\prime \prime }\left (0\right )&=-14\\ y^{\prime \prime \prime }\left (0\right )&=-62 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 25

dsolve([diff(y(x),x$4)-6*diff(y(x),x$3)+7*diff(y(x),x$2)+6*diff(y(x),x)-8*y(x)=0,y(0) = -2, D(y)(0) = -8, (D@@2)(y)(0) = -14, (D@@3)(y)(0) = -62],y(x), singsol=all)
 

\[ y = -4 \,{\mathrm e}^{x}-{\mathrm e}^{4 x}+2 \,{\mathrm e}^{-x}+{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{D[y[x],{x,4}]-6*D[y[x],{x,3}]+7*D[y[x],{x,2}]+6*D[y[x],x]-8*y[x]==0,{y[0]==-2,Derivative[1][y][0] ==-8,Derivative[2][y][0] ==-14,Derivative[3][y][0]==-62}},y[x],x,IncludeSingularSolutions -> True]
 

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