35.8.14 problem 14

Internal problem ID [6221]
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
Date solved : Monday, January 27, 2025 at 01:48:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 26

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

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