73.17.41 problem 41

Internal problem ID [15575]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 08:02:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=2 \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=2*cos(2*x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-3 x}+\frac {10 \cos \left (2 x \right )}{169}+\frac {24 \sin \left (2 x \right )}{169} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==2*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {24}{169} \sin (2 x)+\frac {10}{169} \cos (2 x)+e^{-3 x} (c_2 x+c_1) \]