85.36.7 problem 3 (c)

Internal problem ID [22735]
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 171
Problem number : 3 (c)
Date solved : Thursday, October 02, 2025 at 09:14:11 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = \sin \left (x \right ) c_1 -\cos \left (x \right ) c_2 +\frac {\cos \left (2 x \right )}{6}+c_3 \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 27

ode=D[y[x],{x,3}]+D[y[x],{x,1}]==Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.110 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (x \right )} + C_{3} \cos {\left (x \right )} + \frac {\cos {\left (2 x \right )}}{6} \]