74.10.17 problem 17

Internal problem ID [16143]
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 : 17
Date solved : Thursday, March 13, 2025 at 07:52:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }-y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 12

ode:=3*diff(diff(y(t),t),t)-diff(y(t),t) = 0; 
ic:=y(0) = 0, D(y)(0) = 7; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -21+21 \,{\mathrm e}^{\frac {t}{3}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 16

ode=3*D[y[t],{t,2}]-D[y[t],t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==7}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 21 \left (e^{t/3}-1\right ) \]

✓ Sympy. Time used: 0.132 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 7} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 21 e^{\frac {t}{3}} - 21 \]