43.4.8 problem 2(a)

Internal problem ID [8905]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 2(a)
Date solved : Tuesday, September 30, 2025 at 05:59:56 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 )&=1 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {1}{5} e^{-3 x} \left (3 e^{5 x}+2\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 19

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): 1, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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