89.23.22 problem 22

Internal problem ID [24826]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 22
Date solved : Thursday, October 02, 2025 at 10:48:22 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x) = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\left (1+c_2 \right ) \cos \left (x \right )+\frac {\left (2 c_1 -x \right ) \sin \left (x \right )}{2}+c_3 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to -\frac {1}{2} (1+2 c_2) \cos (x)+\left (-\frac {x}{2}+c_1\right ) \sin (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 17

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

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