44.1.34 problem 7

Internal problem ID [9092]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 06:03:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=2*diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-5*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=2*D[y[x],{x,3}]+D[y[x],{x,2}]-5*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.098 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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