48.3.15 problem Example 3.44

Internal problem ID [7539]
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 : Monday, January 27, 2025 at 03:04:52 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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 35

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

\[ y = -\frac {\cos \left (3 x \right )}{195}-\frac {8 \sin \left (3 x \right )}{195}+c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-2 x}+c_3 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 44

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

\[ y(x)\to -\frac {8}{195} \sin (3 x)-\frac {1}{195} \cos (3 x)+e^{-3 x} \left (e^x \left (c_3 e^x+c_2\right )+c_1\right ) \]