20.8.7 problem Problem 7

Internal problem ID [3740]
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 7
Date solved : Monday, January 27, 2025 at 07:57:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 34

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

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