90.13.14 problem 14

Internal problem ID [25226]
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 : 14
Date solved : Thursday, October 02, 2025 at 11:59:07 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ y^{\prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)-10*y(t) = 0; 
ic:=[y(0) = 5, D(y)(0) = 4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{5 t}+3 \,{\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

ode=D[y[t],{t,2}]-3*D[y[t],{t,1}]-10*y[t]==0; 
ic={y[0]==5,Derivative[1][y][0] ==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-2 t} \left (2 e^{7 t}+3\right ) \end{align*}

✓ Sympy. Time used: 0.128 (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 = {y(0): 5, Subs(Derivative(y(t), t), t, 0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{5 t} + 3 e^{- 2 t} \]