12.17.2 problem section 9.1, problem 3

Internal problem ID [2108]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.1. Page 471
Problem number : section 9.1, problem 3
Date solved : Monday, January 27, 2025 at 05:42:32 AM
CAS classification : [[_high_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-6\\ y^{\prime \prime }\left (0\right )&=10\\ y^{\prime \prime \prime }\left (0\right )&=-36 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 29

dsolve([diff(y(x),x$4)+diff(y(x),x$3)-7*diff(y(x),x$2)-diff(y(x),x)+6*y(x)=0,y(0) = 5, D(y)(0) = -6, (D@@2)(y)(0) = 10, (D@@3)(y)(0) = -36],y(x), singsol=all)
 

\[ y = \left (-{\mathrm e}^{5 x}+2 \,{\mathrm e}^{4 x}+3 \,{\mathrm e}^{2 x}+1\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,4}]+D[y[x],{x,3}]-7*D[y[x],{x,2}]-D[y[x],x]+6*y[x]==0,{y[0]==5,Derivative[1][y][0] ==-6,Derivative[2][y][0] ==10,Derivative[3][y][0]==-36}},y[x],x,IncludeSingularSolutions -> True]
 

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