89.12.5 problem 5

Internal problem ID [24559]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 121
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:46:06 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = c_1 +c_2 x +c_3 \,{\mathrm e}^{2 x}+c_4 \,{\mathrm e}^{-\frac {x}{2}} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to 4 c_1 e^{-x/2}+\frac {1}{4} c_2 e^{2 x}+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 20

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

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