Internal problem ID [4367]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y-26 \,{\mathrm e}^{3 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=26*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) {\mathrm e}^{-2 x} c_{2} +\cos \left (x \right ) {\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 27
DSolve[y''[x]+4*y'[x]+5*y[x]==26*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{5 x}+c_2 \cos (x)+c_1 \sin (x)\right ) \\ \end{align*}