49.4.9 problem 2(b)

Internal problem ID [7620]
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(b)
Date solved : Sunday, March 30, 2025 at 12:17:19 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 )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{5} e^{-3 x} \left (e^{5 x}-1\right ) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 17

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

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