89.11.25 problem 25

Internal problem ID [24550]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 25
Date solved : Thursday, October 02, 2025 at 10:46:03 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x) = 0; 
ic:=[y(0) = 4, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x}+3 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to e^{-x} \left (e^{4 x}+3\right ) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = 0 \]