74.11.12 problem 24

Internal problem ID [16262]
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
Date solved : Tuesday, January 28, 2025 at 08:59:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = \frac {\left (\left (156 t +63\right ) \cos \left (3 t \right )+\left (104 t +16\right ) \sin \left (3 t \right )\right ) {\mathrm e}^{-2 t}}{2704}+{\mathrm e}^{2 t} \left (\sin \left (3 t \right ) c_{2} +\cos \left (3 t \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 54

DSolve[D[y[t],{t,2}]-4*D[y[t],t]+13*y[t]==2*t*Exp[-2*t]*Sin[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{-2 t} \left (\left (156 t+2704 c_2 e^{4 t}+63\right ) \cos (3 t)+8 \left (13 t+338 c_1 e^{4 t}+2\right ) \sin (3 t)\right )}{2704} \]