Internal problem ID [2329]
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 8.10, Chapter review. page
575
Problem number: Problem 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-4 \cos \left (2 x \right )-3 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=4*cos(2*x)+3*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+c_{1} \cos \relax (x )-\frac {4 \cos \left (2 x \right )}{3}+\frac {3 \,{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 30
DSolve[y''[x]+y[x]==4*Cos[x]*3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {12}{5} e^x (2 \sin (x)+\cos (x))+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}