Internal problem ID [13519]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=2 \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=2*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} c_{2} +{\mathrm e}^{-3 x} x c_{1} +\frac {10 \cos \left (2 x \right )}{169}+\frac {24 \sin \left (2 x \right )}{169} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 35
DSolve[y''[x]+6*y'[x]+9*y[x]==2*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {24}{169} \sin (2 x)+\frac {10}{169} \cos (2 x)+e^{-3 x} (c_2 x+c_1) \]