Internal problem ID [2838]
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]]
\[ \boxed {y^{\prime \prime }+y=4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=4*cos(2*x)+3*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -\frac {4 \cos \left (2 x \right )}{3}+\frac {3 \,{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 30
DSolve[y''[x]+y[x]==4*Cos[x]*3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {12}{5} e^x (2 \sin (x)+\cos (x))+c_1 \cos (x)+c_2 \sin (x) \]