20.8.9 problem Problem 9

Internal problem ID [3742]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 9
Date solved : Monday, January 27, 2025 at 07:57:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 36

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

\[ y(x)\to \frac {1}{4} e^{-x} ((1+4 c_2) \cos (2 x)+4 (x+c_1) \sin (2 x)) \]