Internal problem ID [5117]
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 3.43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-\cos \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{-x}-\frac {\cos \left (2 x \right )}{20}+\frac {3 \sin \left (2 x \right )}{20} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 37
DSolve[y''[x]+3*y'[x]+2*y[x]==Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3}{20} \sin (2 x)-\frac {1}{20} \cos (2 x)+e^{-2 x} \left (c_2 e^x+c_1\right ) \\ \end{align*}