89.14.13 problem 13

Internal problem ID [24617]
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 128
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:46:31 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-6*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x}+{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 16

ode=D[y[x],{x,2}]-D[y[x],{x,1}]-6*y[x] ==0; 
ic={y[0]==2,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x}+e^{3 x} \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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