72.17.7 problem 7

Internal problem ID [14943]
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 4.2 page 412
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 07:21:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=3 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+13*y(t)=3*cos(2*t),y(t), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-2 t} \sin \left (3 t \right )+c_{1} {\mathrm e}^{-2 t} \cos \left (3 t \right )+\frac {27 \cos \left (2 t \right )}{145}+\frac {24 \sin \left (2 t \right )}{145} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 47

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

\[ y(t)\to \frac {3}{145} (8 \sin (2 t)+9 \cos (2 t))+c_2 e^{-2 t} \cos (3 t)+c_1 e^{-2 t} \sin (3 t) \]