89.11.19 problem 19

Internal problem ID [24544]
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 117
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:46:00 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime \prime \prime }+23 y^{\prime \prime \prime }+28 y^{\prime \prime }+13 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=6*diff(diff(diff(diff(y(x),x),x),x),x)+23*diff(diff(diff(y(x),x),x),x)+28*diff(diff(y(x),x),x)+13*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{-\frac {x}{2}}+c_3 \,{\mathrm e}^{-x}+c_4 \,{\mathrm e}^{-\frac {x}{3}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 40

ode=6*D[y[x],{x,4}] +23*D[y[x],{x,3}] +28*D[y[x],{x,2}] +13*D[y[x],x] +2*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_1 e^{5 x/3}+c_2 e^{3 x/2}+c_4 e^x+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) + 13*Derivative(y(x), x) + 28*Derivative(y(x), (x, 2)) + 23*Derivative(y(x), (x, 3)) + 6*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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