74.10.18 problem 18

Internal problem ID [16144]
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 : 18
Date solved : Thursday, March 13, 2025 at 07:53:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)+diff(y(t),t)-12*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = 7; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {\left (19 \,{\mathrm e}^{7 t}+2\right ) {\mathrm e}^{-4 t}}{7} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 23

ode=D[y[t],{t,2}]+D[y[t],t]-12*y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==7}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{7} e^{-4 t} \left (19 e^{7 t}+2\right ) \]

✓ Sympy. Time used: 0.159 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-12*y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 7} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {19 e^{3 t}}{7} + \frac {2 e^{- 4 t}}{7} \]