8.13 problem 13

Internal problem ID [4368]

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]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y-26 \,{\mathrm e}^{3 x}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (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)
 

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

Solution by Mathematica

Time used: 0.007 (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*}