68.10.16 problem 16

Internal problem ID [17508]
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 : Thursday, October 02, 2025 at 02:24:53 PM
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*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 10

ode:=diff(diff(y(t),t),t)-diff(y(t),t) = 0; 
ic:=[y(0) = 3, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 12

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

\begin{align*} y(t)&\to 2 e^t+1 \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{t} + 1 \]