6.17.2 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 : Tuesday, September 30, 2025 at 05:24:08 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*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)-diff(y(x),x)+6*y(x) = 0; 
ic:=[y(0) = 5, D(y)(0) = -6, (D@@2)(y)(0) = 10, (D@@3)(y)(0) = -36]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{-x}+{\mathrm e}^{-3 x}+2 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to e^{-3 x}+3 e^{-x}+2 e^x-e^{2 x} \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {y(0): 5, Subs(Derivative(y(x), x), x, 0): -6, Subs(Derivative(y(x), (x, 2)), x, 0): 10, Subs(Derivative(y(x), (x, 3)), x, 0): -36} 
dsolve(ode,func=y(x),ics=ics)
 

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