89.11.10 problem 10

Internal problem ID [24535]
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 : 10
Date solved : Thursday, October 02, 2025 at 10:45:57 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }-49 y^{\prime }-60 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=4*diff(diff(diff(y(x),x),x),x)-49*diff(y(x),x)-60*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {3 x}{2}}+c_2 \,{\mathrm e}^{4 x}+c_3 \,{\mathrm e}^{-\frac {5 x}{2}} \]

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

ode=4*D[y[x],{x,3}] -49*D[y[x],x] -60*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-5 x/2} \left (c_2 e^x+c_3 e^{13 x/2}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-60*y(x) - 49*Derivative(y(x), x) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {5 x}{2}} + C_{2} e^{- \frac {3 x}{2}} + C_{3} e^{4 x} \]