12.18.18 problem section 9.2, problem 18

Internal problem ID [2132]
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 18
Date solved : Tuesday, March 04, 2025 at 01:50:39 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=22 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 25

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(y(x),x)-4*y(x) = 0; 
ic:=y(0) = 6, D(y)(0) = 3, (D@@2)(y)(0) = 22; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 27

ode=D[y[x],{x,3}]-2*D[y[x],x]-4*y[x]==0; 
ic={y[0]==6,Derivative[1][y][0] ==3,Derivative[2][y][0] ==22}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.220 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 3, Subs(Derivative(y(x), (x, 2)), x, 0): 22} 
dsolve(ode,func=y(x),ics=ics)
 

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