Internal problem ID [4360]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y-10 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x} \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x} \sin \left (x \right )+{\mathrm e}^{-x} \cos \left (x \right ) c_{1} +\left (3 x \sin \left (x \right )+3 \cos \left (x \right )\right ) {\mathrm e}^{-x}+2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.101 (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*}