72.16.3 problem 3

Internal problem ID [14899]
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 : 3
Date solved : Tuesday, January 28, 2025 at 07:19:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(t),t$2)-diff(y(t),t)-2*y(t)=5*exp(3*t),y(t), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{2 t}+\frac {5 \,{\mathrm e}^{3 t}}{4} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 31

DSolve[D[y[t],{t,2}]-D[y[t],t]-2*y[t]==5*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {5 e^{3 t}}{4}+c_1 e^{-t}+c_2 e^{2 t} \]