72.16.6 problem 6

Internal problem ID [14902]
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 : 6
Date solved : Tuesday, January 28, 2025 at 07:19:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 31

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

\[ y(t)\to e^{-5 t} \left (e^{3 t} \left (\frac {t}{3}-\frac {1}{9}+c_2\right )+c_1\right ) \]