89.12.17 problem 17

Internal problem ID [24571]
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 121
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:46:10 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\left (5\right )}-23 y^{\prime \prime \prime }-33 y^{\prime \prime }-17 y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=4*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-23*diff(diff(diff(y(x),x),x),x)-33*diff(diff(y(x),x),x)-17*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (c_1 \,{\mathrm e}^{4 x}+\left (c_3 x +c_2 \right ) {\mathrm e}^{\frac {x}{2}}+c_5 x +c_4 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 41

ode=4*D[y[x],{x,5}]-23*D[y[x],{x,3}]-33*D[y[x],{x,2}]-17*D[y[x],{x,1}]- 3*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (e^{x/2} (c_2 x+c_1)+c_4 x+c_5 e^{4 x}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.166 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) - 17*Derivative(y(x), x) - 33*Derivative(y(x), (x, 2)) - 23*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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