48.3.14 problem Example 3.43

Internal problem ID [7538]
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
Date solved : Monday, January 27, 2025 at 03:04:50 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = -c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{-x}+\frac {3 \sin \left (2 x \right )}{20}-\frac {\cos \left (2 x \right )}{20} \]

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 37

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

\[ y(x)\to \frac {3}{20} \sin (2 x)-\frac {1}{20} \cos (2 x)+e^{-2 x} \left (c_2 e^x+c_1\right ) \]