89.15.3 problem 3

Internal problem ID [24637]
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 : 3
Date solved : Thursday, October 02, 2025 at 10:46:39 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }+2 y&=5 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x)+2*y(x) = 5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5}{2}+c_1 \,{\mathrm e}^{-x}+c_2 \,{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 59

ode=D[y[x],{x,3}]+D[y[x],{x,1}]+2*y[x]==5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 e^{-x}+c_2 e^{x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )+\frac {5}{2} \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 39

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

\[ y{\left (x \right )} = C_{3} e^{- x} + \left (C_{1} \sin {\left (\frac {\sqrt {7} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {7} x}{2} \right )}\right ) e^{\frac {x}{2}} + \frac {5}{2} \]