72.16.12 problem 12

Internal problem ID [14908]
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 : 12
Date solved : Tuesday, January 28, 2025 at 07:19:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \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: 0.023 (sec). Leaf size: 22

dsolve([diff(y(t),t$2)+7*diff(y(t),t)+10*y(t)=exp(-2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\left (-1+3 t \right ) {\mathrm e}^{-2 t}}{9}+\frac {{\mathrm e}^{-5 t}}{9} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 27

DSolve[{D[y[t],{t,2}]+7*D[y[t],t]+10*y[t]==Exp[-2*t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{9} e^{-5 t} \left (e^{3 t} (3 t-1)+1\right ) \]