89.11.14 problem 14

Internal problem ID [24539]
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 : 14
Date solved : Thursday, October 02, 2025 at 10:45:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=4*diff(diff(diff(y(x),x),x),x)-13*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {7 x}{2}}+c_3 \,{\mathrm e}^{x}+c_1 \right ) {\mathrm e}^{-\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to e^{-3 x/2} \left (c_2 e^x+c_3 e^{7 x/2}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 24

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

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