89.11.20 problem 20

Internal problem ID [24545]
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 : 20
Date solved : Thursday, October 02, 2025 at 10:46:00 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-45 y^{\prime \prime }-70 y^{\prime }-24 y&=0 \end{align*}

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

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-45*diff(diff(y(x),x),x)-70*diff(y(x),x)-24*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{-\frac {x}{2}}+c_3 \,{\mathrm e}^{4 x}+c_4 \,{\mathrm e}^{-\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 42

ode=4*D[y[x],{x,4}] -45*D[y[x],{x,2}] -70*D[y[x],x] -24*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_1 e^{x/2}+c_2 e^{3 x/2}+c_4 e^{6 x}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*y(x) - 70*Derivative(y(x), x) - 45*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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