35.8.6 problem 6

Internal problem ID [6213]
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 : 6
Date solved : Monday, January 27, 2025 at 01:47:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=10*exp(x)+6*exp(-x)*cos(x),y(x), singsol=all)
 

\[ y = \left (\left (c_{1} +3\right ) \cos \left (x \right )+3 \left (x +\frac {c_{2}}{3}\right ) \sin \left (x \right )\right ) {\mathrm e}^{-x}+2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+2*y[x]==10*Exp[x]+6*Exp[-x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-x} \left (4 e^{2 x}+(3+2 c_2) \cos (x)+2 (3 x+c_1) \sin (x)\right ) \]