72.17.13 problem 13

Internal problem ID [14949]
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 : 13
Date solved : Tuesday, January 28, 2025 at 07:23:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \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: 0.045 (sec). Leaf size: 44

dsolve([diff(y(t),t$2)+6*diff(y(t),t)+20*y(t)=-3*sin(2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {3 \,{\mathrm e}^{-3 t} \sqrt {11}\, \sin \left (\sqrt {11}\, t \right )}{1100}-\frac {9 \,{\mathrm e}^{-3 t} \cos \left (\sqrt {11}\, t \right )}{100}-\frac {3 \sin \left (2 t \right )}{25}+\frac {9 \cos \left (2 t \right )}{100} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 61

DSolve[{D[y[t],{t,2}]+6*D[y[t],t]+20*y[t]==-3*Sin[2*t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {3 e^{-3 t} \left (44 e^{3 t} \sin (2 t)+\sqrt {11} \sin \left (\sqrt {11} t\right )-33 e^{3 t} \cos (2 t)+33 \cos \left (\sqrt {11} t\right )\right )}{1100} \]