74.11.37 problem 49

Internal problem ID [16287]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 49
Date solved : Tuesday, January 28, 2025 at 09:00:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-2 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {2}{3}}\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 22

dsolve([diff(y(t),t$2)+2*diff(y(t),t)-3*y(t)=-2,y(0) = 2/3, D(y)(0) = 8],y(t), singsol=all)
 

\[ y = \frac {2 \left (3 \,{\mathrm e}^{4 t}+{\mathrm e}^{3 t}-3\right ) {\mathrm e}^{-3 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]-3*y[t]==-2,{y[0]==2/3,Derivative[1][y][0] ==8}},y[t],t,IncludeSingularSolutions -> True]
 

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