1.11.12 problem 12

Internal problem ID [333]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 03:57:28 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2-\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x) = 2-sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to \frac {1}{2} (4 x+x \sin (x)+\cos (x)-2 c_2 \cos (x)+2 c_1 \sin (x)+2 c_3) \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 20

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

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