Internal problem ID [2260]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y-2 \,{\mathrm e}^{-x} \sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=2*exp(-x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) {\mathrm e}^{-x} c_{2} +{\mathrm e}^{-x} \cos \left (x \right ) c_{1} -{\mathrm e}^{-x} \left (\cos \left (x \right ) x -\sin \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 34
DSolve[y''[x]+2*y'[x]+2*y[x]==2*Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-x} (2 (-x+c_2) \cos (x)+(1+2 c_1) \sin (x)) \\ \end{align*}