Internal problem ID [4369]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y-2 \,{\mathrm e}^{-2 x} \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=2*exp(-2*x)*cos(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} \sin \relax (x ) c_{2}+{\mathrm e}^{-2 x} \cos \relax (x ) c_{1}+\sin \relax (x ) {\mathrm e}^{-2 x} x \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 26
DSolve[y''[x]+4*y'[x]+5*y[x]==2*Exp[-2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} ((1+c_2) \cos (x)+(x+c_1) \sin (x)) \\ \end{align*}