72.16.23 problem 24

Internal problem ID [14919]
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 : 24
Date solved : Tuesday, January 28, 2025 at 07:20:23 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=-8 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 33

dsolve([diff(y(t),t$2)+4*diff(y(t),t)+6*y(t)=-8,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {4 \,{\mathrm e}^{-2 t} \sin \left (\sqrt {2}\, t \right ) \sqrt {2}}{3}+\frac {4 \,{\mathrm e}^{-2 t} \cos \left (\sqrt {2}\, t \right )}{3}-\frac {4}{3} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 44

DSolve[{D[y[t],{t,2}]+4*D[y[t],t]+6*y[t]==-8,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {4}{3} e^{-2 t} \left (-e^{2 t}+\sqrt {2} \sin \left (\sqrt {2} t\right )+\cos \left (\sqrt {2} t\right )\right ) \]