81.14.13 problem 18-26

Internal problem ID [21698]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-26
Date solved : Thursday, October 02, 2025 at 08:00:06 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=\sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 1169

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x)+y(x) = sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.276 (sec). Leaf size: 2163

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

Too large to display

✓ Sympy. Time used: 0.293 (sec). Leaf size: 245

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

\[ y{\left (x \right )} = C_{1} e^{\frac {\sqrt [3]{6} x \left (- \frac {2 \sqrt [3]{3}}{\sqrt [3]{9 + \sqrt {93}}} + \sqrt [3]{2} \sqrt [3]{9 + \sqrt {93}}\right )}{12}} \sin {\left (\frac {\sqrt [3]{2} \sqrt [6]{3} x \left (\frac {6}{\sqrt [3]{9 + \sqrt {93}}} + \sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{9 + \sqrt {93}}\right )}{12} \right )} + C_{2} e^{\frac {\sqrt [3]{6} x \left (- \frac {2 \sqrt [3]{3}}{\sqrt [3]{9 + \sqrt {93}}} + \sqrt [3]{2} \sqrt [3]{9 + \sqrt {93}}\right )}{12}} \cos {\left (\frac {\sqrt [3]{2} \sqrt [6]{3} x \left (\frac {6}{\sqrt [3]{9 + \sqrt {93}}} + \sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{9 + \sqrt {93}}\right )}{12} \right )} + C_{3} e^{- \frac {\sqrt [3]{6} x \left (- \frac {2 \sqrt [3]{3}}{\sqrt [3]{9 + \sqrt {93}}} + \sqrt [3]{2} \sqrt [3]{9 + \sqrt {93}}\right )}{6}} + \frac {\sin {\left (3 x \right )}}{577} + \frac {24 \cos {\left (3 x \right )}}{577} \]