89.15.5 problem 5

Internal problem ID [24639]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Oral Exercises at page 131
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:46:39 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+y(x) = 3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 x +c_1 \right ) \cos \left (x \right )+3+\left (c_4 x +c_2 \right ) \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 27

ode=D[y[x],{x,4}]+2*D[y[x],{x,2}]+y[x]==3; 
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)+3 \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 20

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

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