Internal problem ID [2263]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial
Solutions. page 529
Problem number: Problem 10.
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 }+10 y-24 \,{\mathrm e}^{x} \cos \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+10*y(x)=24*exp(x)*cos(3*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \sin \left (3 x \right ) c_{2}+{\mathrm e}^{x} \cos \left (3 x \right ) c_{1}+\frac {4 \,{\mathrm e}^{x} \cos \left (3 x \right )}{3}+4 \sin \left (3 x \right ) x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 36
DSolve[y''[x]-2*y'[x]+10*y[x]==24*Exp[x]*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^x ((2+3 c_2) \cos (3 x)+3 (4 x+c_1) \sin (3 x)) \\ \end{align*}