72.16.1 problem 1

Internal problem ID [14897]
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 : 1
Date solved : Tuesday, January 28, 2025 at 07:19:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{4 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(t),t$2)-diff(y(t),t)-6*y(t)=exp(4*t),y(t), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{6 t}+6 c_{2} {\mathrm e}^{5 t}+6 c_{1} \right ) {\mathrm e}^{-2 t}}{6} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 31

DSolve[D[y[t],{t,2}]-D[y[t],t]-6*y[t]==Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{4 t}}{6}+c_1 e^{-2 t}+c_2 e^{3 t} \]