Internal problem ID [14530]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+13 y=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(t),t$2)-4*diff(y(t),t)+13*y(t)=2*t*exp(-2*t)*sin(3*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left (156 t +63\right ) \cos \left (3 t \right )+\left (104 t +16\right ) \sin \left (3 t \right )\right ) {\mathrm e}^{-2 t}}{2704}+{\mathrm e}^{2 t} \left (c_{1} \cos \left (3 t \right )+c_{2} \sin \left (3 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 54
DSolve[y''[t]-4*y'[t]+13*y[t]==2*t*Exp[-2*t]*Sin[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{-2 t} \left (\left (156 t+2704 c_2 e^{4 t}+63\right ) \cos (3 t)+8 \left (13 t+338 c_1 e^{4 t}+2\right ) \sin (3 t)\right )}{2704} \]