68.18.15 problem 21

Internal problem ID [17859]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 21
Date solved : Thursday, October 02, 2025 at 02:28:57 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.082 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(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)
 

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