89.11.9 problem 9

Internal problem ID [24534]
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 : 9
Date solved : Thursday, October 02, 2025 at 10:45:57 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: 23

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);
 

\[ y = \left (c_3 \,{\mathrm e}^{\frac {7 x}{2}}+c_1 \,{\mathrm e}^{\frac {5 x}{2}}+c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 34

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^{-2 x} \left (c_1 e^{5 x/2}+c_2 e^{7 x/2}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.093 (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)
 

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