72.16.4 problem 4

Internal problem ID [14900]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 07:19:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&={\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+13*y(t)=exp(-t),y(t), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-2 t} \sin \left (3 t \right )+c_{1} {\mathrm e}^{-2 t} \cos \left (3 t \right )+\frac {{\mathrm e}^{-t}}{10} \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 76

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

\[ y(t)\to e^{-2 t} \left (\cos (3 t) \int _1^t-\frac {1}{3} e^{K[2]} \sin (3 K[2])dK[2]+\sin (3 t) \int _1^t\frac {1}{3} e^{K[1]} \cos (3 K[1])dK[1]+c_2 \cos (3 t)+c_1 \sin (3 t)\right ) \]