Internal problem ID [5118]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y-2 \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (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)
\[ y \relax (x ) = -\frac {\cos \left (3 x \right )}{195}-\frac {8 \sin \left (3 x \right )}{195}+c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 44
DSolve[y'''[x]+6*y''[x]+11*y'[x]+6*y[x]==2*Sin[3*x],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*}