78.1.47 problem 8

Internal problem ID [18031]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 8
Date solved : Monday, March 31, 2025 at 04:57:18 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);
 

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

✓ 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]
 

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

✓ Sympy. Time used: 0.161 (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)
 

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