75.4.9 problem 9

Internal problem ID [19948]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 48
Problem number : 9
Date solved : Thursday, October 02, 2025 at 05:04:24 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = \left (c_4 x +c_2 \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_3 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to (c_2 x+c_1) \cos (x)+(c_4 x+c_3) \sin (x) \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 19

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

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