89.14.26 problem 26

Internal problem ID [24630]
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 128
Problem number : 26
Date solved : Thursday, October 02, 2025 at 10:46:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-24 y^{\prime \prime \prime }+35 y^{\prime \prime }+6 y^{\prime }-9 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-24*diff(diff(diff(y(x),x),x),x)+35*diff(diff(y(x),x),x)+6*diff(y(x),x)-9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x}{2}} \left (\left (c_4 x +c_3 \right ) {\mathrm e}^{\frac {7 x}{2}}+c_2 \,{\mathrm e}^{x}+c_1 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 37

ode=4*D[y[x],{x,4}]-24*D[y[x],{x,3}]+35*D[y[x],{x,2}]+6*D[y[x],{x,1}]-9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x/2} \left (c_2 e^x+e^{7 x/2} (c_4 x+c_3)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*y(x) + 6*Derivative(y(x), x) + 35*Derivative(y(x), (x, 2)) - 24*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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