90.13.6 problem 6

Internal problem ID [25218]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 235
Problem number : 6
Date solved : Thursday, October 02, 2025 at 11:59:02 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)-10*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{7 t}+c_1 \right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

ode=D[y[t],{t,2}]-3*D[y[t],t]-10*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-2 t} \left (c_2 e^{7 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-10*y(t) - 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{5 t} \]