44.10.15 problem 4(b)

Internal problem ID [9270]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 4(b)
Date solved : Tuesday, September 30, 2025 at 06:15:56 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: 60.013 (sec). Leaf size: 59

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 \int _1^x\left (-\frac {1}{2} \sin (K[2]) \cos ^2(K[2])+c_1 \cos (K[2])+\int _1^{K[2]}-\sin ^2(K[1])dK[1] \cos (K[2])+c_2 \sin (K[2])\right )dK[2]+c_3 \end{align*}

✓ Sympy. Time used: 0.092 (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)
 

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