73.15.33 problem 22.10 (f)

Internal problem ID [15464]
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 (f)
Date solved : Tuesday, January 28, 2025 at 07:56:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=8 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=8*exp(-3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} +4 \,{\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==8*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^x \cos (x)+c_1 e^x \sin (x)+4\right ) \]