85.53.6 problem 1 (f)

Internal problem ID [22819]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 197
Problem number : 1 (f)
Date solved : Thursday, October 02, 2025 at 09:14:56 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to \frac {1}{4} \left (2 \left (x^2+2 c_3\right )-2 (x+1+2 c_2) \cos (x)+(-2 x+3+4 c_1) \sin (x)\right ) \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (x \right )} + C_{3} \cos {\left (x \right )} + \frac {x^{2}}{2} - \frac {\sqrt {2} x \sin {\left (x + \frac {\pi }{4} \right )}}{2} \]