8.6 problem 6

Internal problem ID [4361]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+2 y-10 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x} \cos \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 40

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)
 

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

Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 41

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

\begin{align*} 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 ) \\ \end{align*}