7.10.28 problem 28

Internal problem ID [298]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 28
Date solved : Tuesday, March 04, 2025 at 11:07:29 AM
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: 0.004 (sec). Leaf size: 23

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);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 87

ode=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]
 

\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-5 \text {$\#$1}-2\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-5 \text {$\#$1}-2\&,1\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-5 \text {$\#$1}-2\&,3\right ]\right ) \]

✓ Sympy. Time used: 0.175 (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)
 

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