74.10.13 problem 13

Internal problem ID [16139]
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 : 13
Date solved : Thursday, March 13, 2025 at 07:52:51 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=7*diff(diff(y(t),t),t)+4*diff(y(t),t)-3*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_{1} {\mathrm e}^{\frac {10 t}{7}}+c_{2} \right ) {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=7*D[y[t],{t,2}]+4*D[y[t],t]-3*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 e^{3 t/7}+c_2 e^{-t} \]

✓ Sympy. Time used: 0.157 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) + 4*Derivative(y(t), t) + 7*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- t} + C_{2} e^{\frac {3 t}{7}} \]