Internal problem ID [3254]
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]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+10 y=3 \,{\mathrm e}^{-3 x} x -2 \cos \left (x \right ) {\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-3 x} \cos \left (x \right ) c_{1} +\frac {\left (-3 \cos \left (x \right )-\sin \left (x \right )\right ) {\mathrm e}^{3 x}}{60}+3 x \,{\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.426 (sec). Leaf size: 46
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]
\[ y(x)\to \frac {1}{60} e^{-3 x} \left (180 x-3 \left (e^{6 x}-20 c_2\right ) \cos (x)-\left (e^{6 x}-60 c_1\right ) \sin (x)\right ) \]