42.3.15 problem Example 3.44

Internal problem ID [8825]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.44
Date solved : Tuesday, September 30, 2025 at 05:52:58 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)+11*diff(y(x),x)+6*y(x) = 2*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\cos \left (3 x \right )}{195}-\frac {8 \sin \left (3 x \right )}{195}+c_1 \,{\mathrm e}^{-3 x}+c_2 \,{\mathrm e}^{-2 x}+c_3 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 44

ode=D[y[x],{x,3}]+6*D[y[x],{x,2}]+11*D[y[x],x]+6*y[x]==2*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {8}{195} \sin (3 x)-\frac {1}{195} \cos (3 x)+e^{-3 x} \left (e^x \left (c_3 e^x+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.163 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 2*sin(3*x) + 11*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 3 x} + C_{2} e^{- 2 x} + C_{3} e^{- x} - \frac {8 \sin {\left (3 x \right )}}{195} - \frac {\cos {\left (3 x \right )}}{195} \]