74.10.16 problem 16

Internal problem ID [16221]
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 : 16
Date solved : Tuesday, January 28, 2025 at 08:57:37 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 10

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

\[ y = 1+2 \,{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 12

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

\[ y(t)\to 2 e^t+1 \]