89.12.18 problem 18

Internal problem ID [24572]
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 : 18
Date solved : Thursday, October 02, 2025 at 10:46:10 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\left (5\right )}-15 y^{\prime \prime \prime }-5 y^{\prime \prime }+15 y^{\prime }+9 y&=0 \end{align*}

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

ode:=4*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-15*diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+15*diff(y(x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (\left (c_2 x +c_1 \right ) {\mathrm e}^{\frac {5 x}{2}}+c_5 \,x^{2}+c_4 x +c_3 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 38

ode=4*D[y[x],{x,5}]-15*D[y[x],{x,3}]-5*D[y[x],{x,2}]+15*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} \left (e^{5 x/2} (c_2 x+c_1)+x (c_5 x+c_4)+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + 15*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) - 15*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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