Internal problem ID [2745]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+10 y-3 x \,{\mathrm e}^{-3 x}+2 \,{\mathrm e}^{3 x} \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+10*y(x)=3*x*exp(-3*x)-2*exp(3*x)*cos(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-3 x} \sin \relax (x ) c_{2}+{\mathrm e}^{-3 x} \cos \relax (x ) c_{1}+\frac {\left (-3 \cos \relax (x )-\sin \relax (x )\right ) {\mathrm e}^{3 x}}{60}+3 x \,{\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 42
DSolve[y''[x]+6*y'[x]+10*y[x]==3*x*Exp[-3*x]-2*Exp[3*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{60} e^{3 x} (\sin (x)+3 \cos (x))+e^{-3 x} (3 x+c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}