81.14.7 problem 18-17

Internal problem ID [21692]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-17
Date solved : Thursday, October 02, 2025 at 08:00:02 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=a \sin \left (b x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 48

ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x) = a*sin(b*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-b c_1 \left (b^{2}+1\right ) {\mathrm e}^{-x}+\cos \left (b x \right ) a +b \left (b^{2}+1\right ) \left ({\mathrm e}^{x} c_2 +c_3 \right )}{b \left (b^{2}+1\right )} \]

✓ Mathematica. Time used: 0.109 (sec). Leaf size: 36

ode=D[y[x],{x,3}]-D[y[x],x]==a*Sin[b*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {a \cos (b x)}{b^3+b}+c_1 e^x-c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 27

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

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