89.13.11 problem 11

Internal problem ID [24594]
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 : 11
Date solved : Thursday, October 02, 2025 at 10:46:23 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+10*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 x +c_3 \,{\mathrm e}^{-x} \sin \left (3 x \right )+c_4 \,{\mathrm e}^{-x} \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.568 (sec). Leaf size: 51

ode=D[y[x],{x,4}]+2*D[y[x],{x,3}]+10*D[y[x],{x,2}] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_4 x+\frac {1}{50} e^{-x} ((3 c_1-4 c_2) \cos (3 x)-(4 c_1+3 c_2) \sin (3 x))+c_3 \end{align*}

✓ Sympy. Time used: 0.043 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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