4.7.3 problem 3

Internal problem ID [1251]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 04:31:42 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=6*diff(diff(y(x),x),x)-diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {5 x}{6}}+c_1 \right ) {\mathrm e}^{-\frac {x}{3}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to e^{-x/3} \left (c_2 e^{5 x/6}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {x}{3}} + C_{2} e^{\frac {x}{2}} \]