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 : Tuesday, March 04, 2025 at 01:50:39 PM
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*}

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

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-diff(y(x),x)+y(x) = 0; 
ic:=y(0) = -2, D(y)(0) = 9, (D@@2)(y)(0) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.189 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): -2, Subs(Derivative(y(x), x), x, 0): 9, Subs(Derivative(y(x), (x, 2)), x, 0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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