12.18.4 problem section 9.2, problem 4

Internal problem ID [2118]
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 4
Date solved : Saturday, March 29, 2025 at 11:48:59 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=2*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{-\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

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

\[ y(x)\to c_1 e^{-3 x/2}+c_2 e^{-x}+c_3 e^x \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {3 x}{2}} + C_{2} e^{- x} + C_{3} e^{x} \]