Internal problem ID [2772]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+10 y=24 \,{\mathrm e}^{x} \cos \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+10*y(x)=24*exp(x)*cos(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (3 c_{1} +4\right ) \cos \left (3 x \right )}{3}+4 \,{\mathrm e}^{x} \sin \left (3 x \right ) \left (x +\frac {c_{2}}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 36
DSolve[y''[x]-2*y'[x]+10*y[x]==24*Exp[x]*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^x ((2+3 c_2) \cos (3 x)+3 (4 x+c_1) \sin (3 x)) \]