73.15.32 problem 22.10 (e)

Internal problem ID [15463]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.10 (e)
Date solved : Tuesday, January 28, 2025 at 07:56:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=24 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=24*sin(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} -\frac {3 \sin \left (3 x \right )}{5}-\frac {9 \cos \left (3 x \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==24*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3}{5} (\sin (3 x)+3 \cos (3 x))+c_2 e^{-2 x} \cos (x)+c_1 e^{-2 x} \sin (x) \]