Internal problem ID [2259]
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 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-3 \,{\mathrm e}^{x} \cos \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+y(x)=3*exp(x)*cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}-\frac {3 \,{\mathrm e}^{x} \left (\cos \left (2 x \right )-2 \sin \left (2 x \right )\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 34
DSolve[y''[x]+y[x]==3*Exp[x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3}{10} e^x (\cos (2 x)-2 \sin (2 x))+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}