74.10.20 problem 20

Internal problem ID [16225]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 08:57:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

dsolve([2*diff(y(t),t$2)-7*diff(y(t),t)-4*y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {2 \,{\mathrm e}^{4 t}}{9}-\frac {2 \,{\mathrm e}^{-\frac {t}{2}}}{9} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 25

DSolve[{2*D[y[t],{t,2}]-7*D[y[t],t]-4*y[t]==0,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2}{9} e^{-t/2} \left (e^{9 t/2}-1\right ) \]