72.17.3 problem 3

Internal problem ID [14939]
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 : 3
Date solved : Tuesday, January 28, 2025 at 07:21:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=sin(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 57

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

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