72.16.10 problem 10

Internal problem ID [14906]
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 : 10
Date solved : Tuesday, January 28, 2025 at 07:19:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)+7*diff(y(t),t)+12*y(t)=3*exp(-t),y(0) = 2, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {15 \,{\mathrm e}^{-3 t}}{2}-6 \,{\mathrm e}^{-4 t}+\frac {{\mathrm e}^{-t}}{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+7*D[y[t],t]+12*y[t]==3*Exp[-t],{y[0]==2,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-4 t} \left (15 e^t+e^{3 t}-12\right ) \]