74.10.19 problem 19

Internal problem ID [16153]
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 : 19
Date solved : Monday, March 31, 2025 at 02:45:07 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)-7*diff(y(t),t)+12*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = -2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 14 \,{\mathrm e}^{3 t}-11 \,{\mathrm e}^{4 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

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

\[ y(t)\to e^{3 t} \left (14-11 e^t\right ) \]

✓ Sympy. Time used: 0.172 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(12*y(t) - 7*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)
 

\[ y{\left (t \right )} = \left (14 - 11 e^{t}\right ) e^{3 t} \]