89.13.16 problem 16

Internal problem ID [24599]
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 127
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:46:25 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime \prime }+11 y^{\prime \prime \prime }-4 y^{\prime \prime }-69 y^{\prime }+34 y&=0 \end{align*}

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

ode:=2*diff(diff(diff(diff(y(x),x),x),x),x)+11*diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)-69*diff(y(x),x)+34*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{6 x}+c_2 \,{\mathrm e}^{\frac {9 x}{2}}+c_3 \sin \left (x \right )+c_4 \cos \left (x \right )\right ) {\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 40

ode=2*D[y[x],{x,4}]+11*D[y[x],{x,3}]-4*D[y[x],{x,2}]-69*D[y[x],{x,1}]+34*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-4 x} \left (c_3 e^{9 x/2}+c_4 e^{6 x}+c_2 \cos (x)+c_1 \sin (x)\right ) \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(34*y(x) - 69*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + 11*Derivative(y(x), (x, 3)) + 2*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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