72.16.21 problem 22

Internal problem ID [14917]
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 : 22
Date solved : Tuesday, January 28, 2025 at 07:20:18 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=2 \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: 0.018 (sec). Leaf size: 18

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=2,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {2 \,{\mathrm e}^{-3 t}}{3}-{\mathrm e}^{-2 t}+\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+6*y[t]==2,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-3 t} \left (e^t-1\right )^2 \left (e^t+2\right ) \]